It says "may" as in "possibly" as in some hotels wont take debit cards upon check in.

I've never had a problem with it, i use a MasterCard debit card through my credit union for priceline/hotwire all the time. I don't think the debit card is the problem - usually when anything refers to a "debit card" not being accepted they mean a card without a visa/mc logo, which is not what the average consumer is carrying.