The synth detective detective is unable to wear synth armor. (Like the dog can wear dog armor.

And when the synth detective is wearing power armor, there is a graphical misplacement, that usually happens almost everytime it fast travel to Sanctuary. It's not possible to see what the companion is doing (perhaps repairing) but parts of the armor is out in the air and first falls in place after a while.

Edit: http://www.nexusmods.com/fallout4/mods/2679/?

Yeah I think the designers were too attached to Nick's gumshoe look to allow you to change it.

There is a good chance the "out of place" power armor is tied into the smoking idle animation Nick and a few others use.

How they smoke while in power armor with helm equipped is anyone's guess though.

Nick is not a "standard" Gen 2 Synth.

He uses a unique model.