I agree and I confirm that the card is not visibly thicker than the plastic card. And if it is actually, it should be some 1/10,000 inches that could not explain what happens in some machines.
The problem could be simply the way how the machines pull the card inside, and push it back:
I think they use small (plastic) rolls to pull/push the cards, the machines were all manufactured for and tested with plastic cards. The friction with the titanium surface could be not enough sometimes.