IMO it's hard to "pretty much fire" someone whose contract of employment has expired.
Perhaps they made a decision to not offer him a contract, and the public expressions about a five year offer being rejected came from a mutual agreement by the parties, so that:
a) the organization would gain a public relations benefit from apparently having offered a popular executive a lengthy contract to stay, and
Anthopoulos would gain the within industry benefit of apparently making a powerful personal decision to refuse the offer (rather than the reality of having not been offered a deal).
I think that's hard to swallow. It takes a lot of assumptions. For one thing, I don't think Shapiro would care all that much about the PR benefit of a fake offer and rejection, because fans would still be mad that AA left and in any event fans tend to get over things like that pretty quickly (coaching / executive changes). Also, I think the "AA saving face" angle is a bit flawed because something like that would be pretty transparent within the industry. These people all talk, and all have webs of contacts within other organizations.
So that leads me to believe that they really did make an offer to AA that he rejected. And I suppose it is possible that they made an offer while hoping that he would reject it, but again, this seems unlikely to me. I doubt they would risk him accepting for significant money if they sincerely wanted him to leave.
IMO, Shapiro sincerely wanted AA to stay as the nominal GM. Shapiro sincerely offered him a contract. Both parties realized that it would be an arguable role reduction, and perhaps Shapiro also told AA about plans to bring in Ross Atkins in some sort of almost parallel role. I think AA chose to reject it for this reason (reduced autonomy) and/or relationship reasons (just flat out doesn't like Shapiro or Ed Rogers or whoever).
I think if we act like rational, reasonable, well-adjusted people, and follow the breadcrumbs of logic, this is where we end up.