It suggests that the outfits are some sort of spell that can be quickly applied, if seconds after being summoned the Death Eaters can arrive in full regalia.

This is a feature of the Mythic Dawn armor in Oblivion, and actually one of the cooler things about the game, I thought--the sleeper agents are dressed and act like normal people, and then BAM, conjured full plate.

And it's not like you would want your agents to be exposed when people rummage through their things.