RFs are not approved under any current legislation and never have been
As defined approved is used to refer to something that is generally or officially accepted as being correct or satisfactory. One was required to apply to become an RTF and those now registered had their applications accepted, or otherwise approved by an authority.
....offered by an approved training organisation or an organisation created with the aim of promoting aerial sport or leisure aviation, for the purpose of attracting new trainees or new members.
An Approved Training Organisation is a proper noun. An
approved training organisation (without capitals) has the meaning of a training organisation that is approved. Had the author of the text meant an ATO he or she should have used a proper noun to make the distinction. Further, by highlighting other types of
organisations that qualify, the writer endorses the view that the word organisation is being used in a general sense.
...that the CAA are of the opinion that these are so badly drafted by EASA that they are unenforceable in law...
Yep!