I used to work with desk and review copies as well. From what I could tell, most publishers will provide review copies for free. However, there were some publishers that would give you the book to review for a time period and if you didn't decide to adopt it, they'd expect you to either pay for it or return it. If I remember correctly, those usually came with an invoice right away.
That's why it was my policy to only order desk copies for established textbooks. If a professor wanted a review copy, they had to be a part of the committee looking to decide which book would work best for a certain class. Luckily, that was an easy policy for me to have because individual professors didn't make the textbook decision on their own and there would always be a committee. If there wasn't, then I knew it was a personal request.
If a professor just wanted to get a review copy to take a look at it, I would give them the contact information for the publisher/rep and they could order it on their own. I don't mind a professor trying to game the system but I didn't want to have to answer the questions that would come if I were the one abusing that review copy privilege. Publishers do watch that kind of thing. If there was a problem then I could send them directly to the person they had been shipping the books to.
To sum it up, you're probably in the clear but you may have to inform the professor that if the publisher tries to charge you, the books are going back or his department is paying for them.