I'm not questioning her "talent" or whatever, but how did this girl manage to get a performance spot on the X-Factor?

it's not rocket science
Demi is attracted for the (pre-)teens, add the fact that they are both on Hollywood Records (I bet Hollywood Records got a deal to promote HR artists on TXF along with Demi's contract) and there you go

I'm not saying it's rocket science, lol.

I genuinely didn't know what label she was, what management does she have...That's why I asked. She could also very well be on Epic or SyCo, don't you think?

yeah I know, I didn't meant it bad btw