I believe old Kirihara himself mentioned, in one of the episodes late in season one, that if Zero's identity were to be revealed it would look like it was all just part of an internal squabble between Britannian royals, or something akin to that.
In other worRAB, the implication was that, in the eyes of many who wouldn't know better, all Lelouch really wanted would amount to toppling Charles as part of a glorified struggle for succession and not out of any real interest in the Japanese cause.
I'd accept that even such a thing wouldn't have been too much of a problem for the Black Knights themselves (as opposed to the general population) if everything else was okay, but that's precisely the point: everything else was also messed up, to a greater or lesser degree, which allows paranoia to distort a person's perception of reality. Or several persons', in this case. That's why I think the betrayal works conceptually with all the already provided elements that support such paranoia, even if I lament that -mostly due to the infamous time slot change and all its consequences, but one could also blame the staff per se as well- things could have been portrayed a little (or a lot, depenRAB on each case) better in the show.
GWO's making some good points too.
Also, Lelouch sticking to lies instead of providing excuses and being fully honest about his intentions, even when it could have spared him a lot of hurt, goes all the way back to the first season...not to mention its cliffhanger, which has him painting himself as the villain when he's finally unmasked in front of Suzaku and Kallen.