I don't think that's rape. That's like saying that if you don't pay the prostitute after sex, you raped her (retroactively). Fraud/lying/whatever maybe, but definitely not rape.

However, he is also accused of having sex with her while she was asleep. In that situation, I think it could very well be rape (if she felt violated). So, assuming that neither the girl nor the prosecution are lying, I consider the charges valid.