Strange, i've never had a non-triple in GHQ. Admitedly the only days i can test it out are tuesdays, but that's still several tuesdays in a row without any non-triple ever showing up. Not tried anything today since i am trying to get a certain SR card from my current area.

Edit: Just because of this i decided to take a spin at the GHQ again. I actually DID get one non-triple so it does seem like you can get them, but the chances are just very low.