I went to the South Boston Military Checkpoint and in the cage there looked like X-01 power armor, but when I hovered the mouse over it all it said was "T-60".

I DO have pictures, but "my media library" I guess cant take pictures from my screenshots folder?

Yeah, that's the way the game seems to handle those suits.

What you get can be dependent on the level you are at when you first visit a particular area.

Sometimes you can get a companion to enter an abandoned suit and what looks like a complete outfit suddenly deteriorates before your eyes after they enter it because parts are actually damaged or missing.

I was level 40 when I saw that suit. A full suit of X-01, but...it just...changed? :X

I'd love to post a picture or two but I don't know how.