Then someone decided that was trigonometrically wrong.
There's nothing trigonometrically wrong (or wrong at all, for that matter) with basing sight adjustments and target measurements on inches.
It is, however, incorrect to state that 1 MOA is equal to 1" at 100 yards. It's only approximately equal to 1". It's incorrect in exactly the same way it would be incorrect to claim that 1" is equal to 1.047198... It's incorrect in more or less the same way as it would be incorrect to say that 100 yards is equal to 100 meters--they're pretty close to each other--but not equal.
1MOA is simply not the same thing as 1" at 100 yards. It's reasonable to say that the two things are close enough for practical purposes that it's acceptable to approximate 1MOA as 1" in most cases. It would even be reasonable to use that approximation as a standard in the shooting sports--although I know of no official statement of such a standard.
It's not that any one suddenly decided something about minutes of angle or inches. An MOA (minute of angle) has a definition that was established long before someone decided to express shot groups in terms of minutes of angle. Just as the inch measurement had a definition before the first European shooter ever measured a shot group in inches.
So sure, it's fine to approximate 1 MOA as 1" at 100 yards for practical purposes. Just as it's fine to approximate pi as 3 for some applications--in fact, the two approximations are identical. Just as it's fine, in many cases, to approximate 100 yards as 100 meters. But that doesn't mean pi IS actually 3, or that 100 yards is actually equal to 100 meters, and it doesn't mean that 1 MOA is actually 1" at 100 yards. It's just close enough that many folks don't care about the difference.