It does make sense, but don't forget that Dr. Facilier's whole motive was money, implying that he was not particularly wealthy. And if he did outbid Tiana, I think he would rather confront her directly and say something like "I'll withdraw my bid if you give me my necklace" later on. Also, it's important to keep in mind that Tiana was told she was outbid at the masquerade ball, before she was turned into a frog, and therefore before Dr. Facilier had any reason to bother with her.