So my companion is trapped inside the room with the guy from the Legion. Is there a way to get him out?

I had the same issue. Luckily I anticipated a problem and saved just before entering. Just had them wait outside since EDE cannot have its weapons removed.

See, thats just the thing, I did have them both waiting, but he (Boon) came in with a switchblade anyway...

Also, they didn't remove ALL my weapons, I still had a silenced .22 on me when I was in the room.