I've taken the liberty of highlighting the parts of 141.015 that clearly define training that is given as part of a flight review as being Part 141 training:
:
141.015 Definitions of Part 141 flight training, authorised Part 141 flight training, Part 141 operator and Part 141 certificate
(1) Part 141 flight training is any of the following that is conducted in an aircraft or flight simulation training device:
(f) training, other than training conducted as a multi‑crew operation, that is given as part of a flight review;
Which leads us to 141.050:
141.050 Part 141 flight training—requirement for Part 141 certificate or approval
(1) A person commits an offence if:
(a) the person conducts Part 141 flight training; and
(b) the person does not meet the requirement mentioned in subregulation (2).
Penalty: 50 penalty units.
(2) For paragraph (1)(b), the requirement is that the person must hold:
(a) a Part 141 certificate that authorises the person to conduct the training; or
(b) an approval under regulation 141.035 to conduct the training.
(3) An offence against this regulation is an offence of strict liability.
So yes technically you can get CASA approval conduct training during a flight review outside a Part 141 operation, but you need a 141.035 approval to do so.
141.035 Approvals by CASA for Part 141
(1) If a provision of this Part refers to a person holding an approval under this regulation, the person may apply to CASA, in writing, for the approval.
(2) Subject to regulation 11.055, CASA must grant the approval.
(3) Subregulation 11.055(1B) applies to the granting of an approval under this regulation.
Whilst this seems fairly straightforward, the crunch is you need to obtain a 11.055 approval, and the requirements are quite stringent:
11.055 Grant of authorisation
(1) This regulation applies despite any other provision of these Regulations that provides for the grant or issue of an authorisation, but subject to section 30A and paragraphs 30DY(2)(b), 30DZ(2)(b) and 30EC(2)(b) of the Act.
Note 1: Under section 30A of the Act, the Court may make an order excluding a person from a particular aviation activity for a specified period (the exclusion period). Under subsection 30A(4), during the exclusion period any authorisation granted to the person for the activity is of no effect and a new authorisation to undertake the activity is not to be granted to the person.
Note 2: Under section 30DY of the Act, CASA must give the holder of an authorisation a demerit suspension notice if the holder has incurred at least 12 demerit points in relation to authorisations of the same class in a 3 year period. Under paragraph 30DY(2)(b), the holder is not entitled to be granted a new authorisation of that class during the period of the suspension.
Note 3: Under section 30DZ of the Act, CASA must give the holder of an authorisation a demerit suspension notice if the holder has incurred at least 6 demerit points in relation to authorisations of the same class in a 3 year period and has previously been given a demerit suspension notice in relation to that class of authorisations. Under paragraph 30DZ(2)(b), the holder is not entitled to be granted a new authorisation of that class during the period of the suspension.
Note 4: Under section 30EC of the Act, CASA must give the holder of an authorisation a demerit cancellation notice if the holder has incurred at least 6 demerit points in relation to authorisations of the same class in a 3 year period and has twice previously been given a demerit suspension notice in relation to that class of authorisations. Under paragraph 30EC(2)(b), the holder is not entitled to be granted a new authorisation of that class for 3 years from the date of the notice.
(1A) Subject to subregulations (1B) and (1C), if a person has applied for an authorisation in accordance with these Regulations, CASA may grant the authorisation only if:
(a) the person meets the criteria specified in these Regulations for the grant of the authorisation; and
(b) any other requirements in relation to the person that are specified in these Regulations for the grant of the authorisation are met; and
(c) any other requirements in relation to the thing in respect of which the application is made that are specified in these Regulations for the grant of the authorisation are met; and
(d) these Regulations do not forbid CASA granting the authorisation in the particular case; and
(e) granting the authorisation would not be likely to have an adverse effect on the safety of air navigation.
(1B) If another provision of these Regulations provides that this subregulation applies to the granting of the authorisation, CASA may grant the authorisation only if:
(a) the requirements of paragraphs (1A)(a) to (d) are satisfied; and
(b) granting the authorisation will preserve a level of aviation safety that is at least acceptable.
(1C) If the authorisation is an experimental certificate, CASA may grant the authorisation only if:
(a) the requirements of paragraphs (1A)(a) to (d) are satisfied; and
(b) granting the authorisation would not be likely to have an adverse effect on the safety of other airspace users or persons on the ground or water.
(2) In paragraph (1A)(a), a reference to meeting the criteria for the grant of an authorisation includes (in the case of an applicant who is an individual):
(a) having any qualifications required by or under these Regulations for the grant of the authorisation; and
(b) having any experience required by or under these Regulations for that grant; and
(c) having successfully completed any training required by or under these Regulations for that grant; and
(d) if there is a requirement as to recency or currency of the applicant’s training or experience—meeting that requirement; and
(e) if a standard of medical fitness is required by or under these Regulations for that grant:
(i) having attained that standard; and
(ii) having been granted any medical certificate required; and
(f) if particular attributes of character are required by or under these Regulations for that grant—having those attributes; and
(g) if a standard of proficiency in an activity is required by or under these Regulations for that grant—meeting that standard of proficiency.
(3) If these Regulations limit in any way the number of authorisations of the relevant kind that may be granted, CASA may refuse to grant the authorisation if the limit will be exceeded if the authorisation is granted.
(4) For paragraphs (1A)(e) and (1B)(b), CASA may take into account:
(a) the applicant’s record of compliance with regulatory requirements (in Australia or elsewhere) relating to aviation safety and other transport safety; and
(b) the applicant’s demonstrated attitude towards compliance with regulatory requirements (in Australia or elsewhere) relating to aviation safety and other transport safety; and
(c) the applicant’s experience (if any) in aviation; and
(d) the applicant’s knowledge of the regulatory requirements applicable to civil aviation in Australia; and
(e) the applicant’s history, if any, of serious behavioural problems; and
(f) any conviction (other than a spent conviction, within the meaning of Part VIIC of the Crimes Act 1914) of the applicant (in Australia or elsewhere) for a transport safety offence; and
(g) any evidence held by CASA that the applicant has contravened:
(i) the Act or these Regulations; or
(ii) a law of another country relating to aviation safety; or
(iii) another law (of Australia or of another country) relating to transport safety; and
(h) in the case of an authorisation referred to in subregulation 11.040(2), the applicant’s financial standing and financial stability; and
(i) any other matter relating to the fitness of the applicant to hold the authorisation.
(5) For the application of paragraphs (4)(a) to (i) in relation to an applicant that is a corporation, references to the applicant include each of the officers (other than employees) of the applicant.
(6) For the application of paragraphs (4)(a) to (i) in relation to an applicant that is a member of a partnership, references to the applicant include each of the other members of the partnership.
(7) CASA may grant the authorisation in respect of only some of the matters sought in the application.
I am aware of one independent instructor that I believe has a 141.035 approval. Prior to obtaining the approval he was a HOO, and he is an examinier that can conduct EPCs on other examiners.