Hmm, thinking about it, depending on how widely seen the Romulan is, it might not be a continuity glitch. Kirk, Spock, and Sulu can all know, but Stiles is the one who makes a big deal out of it.

This makes a bit of sense, in that it was made clear in the Next Generation that Spock must have already known anyway - the whole business about reunification pretty much implied that Romulan-Vulcan common ancestry was a commonly known fact already.