This isn't the case. By moving the threshold less and less each time they could keep moving it indefinitely while remaining below a chosen upper bound.

but that would just converge on the chosen upper bound, which suggests that upper bound was the threshold.

Well true but you don't have to accept all the people who reach the final threshold until you've actually raised it all that way, so it allows you to reject more people while avoiding nasty near misses. It also allows you to defer the final decision indefinitely, taking into account only those near misses that actually occur.

For example I reckon you could get it to converge by e.g. accepting anyone who comes closer to the threshold than anyone before, this could avoid all near misses (for some definition of 'near miss') while almost certainly remaining bounded (unproven, ask your local mathematician for advice).

His point is valid though. If the cut off is 100 lbs and allow for 1 lbs more, then it really is is 101 lbs. Someone weighing 102 would still be fired and so on.

Maybe older people have more problem keeping weight off (evolution) so this is also a way to keep them fit and young. I get the BMI thing not being accurate but then, maybe they don't want "big-boned" or muscular women there.