If there are persistent, wide-spread rumors about some ultra-top-secret organization, I'd say there was a better than 50% chance it exists.
I just try to imagine the GTVA explaining this as the reason for the war to their citizens.
We just reopened the Sol-Delta Serpentis jumpnode and our spyprobes have intercepted messages that hint at the existance of a secret black-ops group called the Fedayeen.
We don't know who they really are or what they want or even if they really exist, but since the rumors of their existance are so widespread there is a 50% chance that they really do exist.
Because of that, and some other minor reasons - like our continued survival in the face of the shivan threat or our current socio-political system being on the brink of collapse - we decided to go to war with them.
But the main reason for the war, as stated before, is the possible existance of a black-ops group we know nothing about and aren't even sure exists"
Don't get me wrong, what you say is often right (though not always), but maybe the people of the UEF just enjoy conspiracy theories more than we do now, because they had no real and tangible conflics and conspiracies to occupy their attention (except the one against the GEF) before the GTVA came in guns blazing.
Either way a 50% chance of them even existing can't be enough for it to be the GTVAs main
reason for the war. So either is isn't the main reason at all, or the tevs have more information than they should have been able to get.
But since noone outside of the Fedayeen and the Elders even knows for sure they exist, I can only imagine three theories:
1) The GEFs fed the GTVA some made up "information" about the Fedayeen which the GTVA believed (extremely unlikely, since there was supposed to be no contact what-so-ever before the decition to go to war - besides, why should the GTVA believe terrorists in the first place).
2) A turncoat within the Fedayeen who detected the GTVAs spying and decided to join them.
3) The Fedayeen deliberately leaked information to the GTVA to further some shadowy plan of theirs. This might be the Vishnans testing Humanty, but not wanting their involvment being detectable, so they use their Human agents (and then go silent, either as part of the test, or because Humanity failed it).