I think you're looking at this the wrong way. She isn't trying to give away the slot she offered you because she can make money. She is trying to sort out scheduling. If you don't want to come then she can give another client in need the appointment but she's giving you the option to still come, you have first refusal. Also, you're assuming the other person is a paying client, you don't that for a fact, this other person could be on any number of payment arrangements and even not paying at all currently.

Decide if you want the appointment and get back to her ASAP so that she can sort her scheduling out.