Okay, this has got to be the weirdest thing I have seen ever. I went to the 35 Court building to get a full set of X-01 power armor. After clobbering the Assaultron and Security Bot on the roof, I looked into the chamber and saw that the armor set was the T-60 MkIII. I decided to go ahead and open the chamber. I went and climbed into the suit. The second I switched to third person to check out the armor, it changed from T-60 MkIII armor to X-01 armor. I'm not complaining but holy crap that was both random and really bizzare.

Yes, it is known its an appearence bug for that armor, when you unlock it.

X-01 doesn't appear correctly, until you remove the pieces from the frame and put them back in.

This happens with several suits that you can find. It's most prevalent (or most well known) with 35 Court because it's regarded as an X-01 hot spot (although X-01 can spawn just about anywhere).