Back in the old days, the Medal of Honor had meaning. It was a sign of respect from our leaders and an acknowledgment that the recipient had done something to serve it.
In the Trump era, the Medal of Honor was handed out like bubble gum, and was given by a person of no respect and honor himself (trump).
I imagine that Belichek saw himself as getting tainted honors from a tainted person, and he felt that the medal would always bear some sort of a taint because of that. He also, no doubt, felt he was being used as a populist political puppet.
My guess is that Biden will make a similar offer and Belichek will accept the honor.