Doesn't MLB decide based on length of service?
If so, Moose spent more time in an Oriole uniform then the Yankees.
I thought MLB, changed the process, when Wade Boggs sold his allegiance to Tanpa.
MLB is not involved at all with the Hall of Fame decisions, either the voting or the hat selecting. HoF is independent of MLB. They pick what hat a player will wear based on where the player made their biggest impact, though they do take the player's wishes into consideration.
BTW, Boggs denies that he tried to go into the HoF as a Ray. True or not, the Hall of Fame changed their policy after his induction so that they don't simply defer to the player's choice, a small team of people there make the decision.