An AA elite member can ask to move a non-elite companion on a different PNR to an adjacent seat, even in MCE to which the non-elite is not normally entitled unless they have paid for it. Such movement is allowed; I've had it done many times, and I'm sure others here have too. Given that, it makes sense that a non-elite companion can also board with the elite. Both are basically a perk for the elite, to have their companion nearby. It would be odd if the non-elite boards with the elite but isn't sitting adjacent, but AA can't check everything.

My understanding is that if the elite member is upgraded to a different cabin class, then the adjacent non-elite may be removed by AA from MCE back to standard Economy, although that isn't done automatically (but may be done if, for example, a GA needs the MCE seat and notices the "lone" non-elite there). The rationale is that with the elite now in a different cabin, there is less justification for allowing the non-elite a better seat; adjacency has been lost. Similarly, if the elite is in a different cabin class from the non-elite companion (i.e., not just MCE versus standard Economy), then AA could sensibly disallow simultaneous boarding, although an individual GA may allow it.

I'm not advocating any which way here. I'm just trying to summarize my understanding of the policies for non-elite companion seating and companion boarding, which appear to be related.