AMCs do not use the words 'shall' or 'must', because they are 'soft law' means of compliance with the 'hard law' of the Aircrew Regulation. Alternative Means of Compliance ('AltMoCs) may be proposed, but they have to meet the equivalent safety standards of the EASA or UK AMC.
After considerable lobbying of EASA, AMC1 FCL.740(b) was amended to its current form under Annex II to ED Decision 2018/009/R in 2018; there is no 'three year' rule.
ATOs should be deciding on the amount of refresher training needed on a case-by-case basis. Of course it would be in their financial interest to require an applicant to take the full TR training course and anyone facing such an attitude should challenge the ATO to explain itself - or walk away and find another ATO more prepared to respect the amended AMC!