What I said is that it is up to the FAA "Authorised Instructor" as defined in FAR 61.1b to determine whether to put his name against previously recorded log book entries. This is especially relevent (as I am sure you will agree) when the entire prior training is 100% outside the US and being used to gain an initial certificate.
He is after all, the one putting his reputation on the line.
It is the "Authorised Instructor's" responsiblity to ensure that all the flight requirements of 61.109 are met - not the foreign instructor.
OK, we agree on that one
This issue is moot because practically nobody does a load of training in say Mongolia and then turns up in the USA and asks for a checkride. Everybody turning up in the USA will end up doing some hours in a plane, simply because he won't get signed off otherwise.
Curiously, the
ATPL may be an exception; you can indeed just turn up in the USA with a non-US ATPL and go straight off to do any writtens and the checkride for an FAA license/rating, without an endorsement from an instructor. This is what a colleague was told, by no less than John Lynch himself, IIRC.