Jepp Terminal AU-15 section 1.7.1: "Having arrived over the IAF...". While doesn't actually state that "you must..." I think it is pretty obvious that that is what is required. The intention, I assume, is that the IAF-to-FAF segment positions the aircraft correctly, laterally and speedwise, for the final segment, as well vertically, although that could be achieved independently as you point out.
A DME Arrival is different because the inbound track is not critical, hence the requirement for no manoeuvring only inside the FAF.