That sounds reasonable.I think her remark is that she has no royal blood yet that Square Enix defines her as a Princess disregarding her lack of royality or even nobility.
The "real Alice" was the daugther of a rich and successfull merchant after all. Her purity and the fact that Disney has a fetish for Pincesses are the reasons of Square Enix to call her a "Princess" aswell... if you don't like it call them up and have them change their point of view on the matter.
Feels like that logic should be able to be applied to mulan as well though.
I really have no problem with her being a princess. The more the merrier.