No, they can't.
Yes is can and does.....Any time I have been asked for a major credit card, for hotel, car rental, airplane tickets……my debit card works just fine. They do not seem to know it is a debit card.
So you can charge something to your debate card without the funds ever being removed from your account? Bullshit. Plus you can get miles, cash or other things back from using your credit card, also good.
Debit Cards can be processed as Credit Cards; they don't act the same.