Many of the 'Other' series trophies were from second parties(Custom Robo, Dobutso Bancho/Cubivore, Doshin the Giant, etc.)i am not fully sure of this, but did any other trophy come from a 2nd party developer besides HAL and trophies from the smash characters? if not, then that might be why. if so, maybe sakurai was not in touch with companies outside of japan, and rare was based in europe, so that might be why too.
And you may not have known this, but there is one more reference to a Rare game in Melee. The Motion Sensor Mine and Cloaking Device were both from Perfect Dark(That is the TOP SECRET game).
In general, though, Sakurai just probably didn't think that some of them were more Rare games than Nintendo games.