You can't really trust someone with a foggy memory to get the details right. She also called herself a powerful trainer, which isn't true either. She is the weakest Frontier Brain.
As far as your timelines go, if you really want to get down to straight facts, this is what we know:
RBY, RSE take place in Year 1
GSC, DPP take place in Year 3
FRLG takes place in Year 1
HGSS take place in Year 3
SM take place in Year 10
Anabel coming from Emerald makes sense. Emerald came out in 2004. 3 years later would be 2017, while SM came out in 2016. That means Anabel would have slid into the SM timeline after Emerald but before DP.
Where ORAS truly goes, is a debate of itself.