Had a little free time. Looked on American website.
Looked at flights Leaving LAX July 24, return Aug 1.
There are five different fares, corresponding to different classes and different flexibility (changes and refunds) allowed.
Basic Economy $708
Main Cabin $768
Business Class $1366
Main Cabin (flexible) $3282
Business (flexible) $4082
Maybe this explains why several of us were seeing wildly different fares.