I tend to believe them about the cards being demagnetized, only because the two times I had to get my cards replaced, it wasn't just at the turnstiles, and it wasn't intermittent. Once they stopped working, they did so completely, both at the turnstiles (no big deal because of the bar code), and at all FP machines.
And in my case, it wasn't a credit card in my wallet that they claimed was the culprit, because I didn't have the cards in my wallet, or even in the same pocket as my wallet. They claimed that the cards demagnetized each other, because I had them together (IE touching) in the same passholder booklet.
If anything, I'm inclined to believe the turnstiles or FP machines may be demagnetizing the cards, rather than the cards being just fine and the machines just misreading them now and then. Lord knows they've told me plenty of other things that turned out not to be true. For example, the first time this happened, they told me to be careful because they wouldn't replace it if it happened again - but that didn't stop them from replacing it when it did happen again. And any passholder has heard and read all the dire warnings you get about your pass not being replaceable if you lose or destroy it. But I know at least one person who has gotten her AP replaced several times at guest services just outside the park gates. All they've ever made her do is show her driver's license.
Anyway, I'm sure they have their reasons - but you can't believe everything they tell you, even if "they" is Disney.