From the OP, my understanding is that you purchased the pair of tickets using an AmEx free/discount companion certificate - is that correct?

If so, I can at least say that my AmEx companion certificate states in the T&C that neither person is eligible for upgrade on the itinerary purchased using certificate (additionally, the companion earns no mileage). I've not used one recently to have an at-the-airport experience, so unfortunately I can't provide that - but I do know in searching for itineraries to use the certificate recently, it does show "upgrade requested" up to the purchase screen despite the T&C stating otherwise.

My best guess is the website/res system doesn't pick up the nuance, but the upgrade system does and won't process the requested upgrade because of the certificate.