Trials, or Trails?
Your friend's boyfriend may also be looking for a time trials track bike, which is an entirely different animal. If that's the case, the time trials discipline in track riding doesn't have any more specific requirements than any other track race. Fixed gear, track nuts (not quick releases) on the wheel hubs, and no brakes. However, there's also a discipline in mountain biking that goes by the same name. Unfortunately, a lot more information is needed before it's possible to narrow anything down.