When one considers the nature of Mystery cults seems clear that it could certainly be associated with a knowledge or belief system.
Yet if we're going to use the other mystery cults as examples there are two things that jump out. The first is that the knowledge and belief are very specific. ie not "paganism" but worship of Dean the spirit of Diedneishness and spontaneous magic. the second is that it isn't precisely certain that the Diedne way cult is the only way to get the virtue (although it could be).
If you think about paganism in general all of the non-divine non infernal traditions descend from pagan roots including the order itself (although the order has been secularized). So I'd think that it is inevitable that the Diedne tradition has pagan roots. Just like all of the others.
More out of curiosity than anything else - why do you think that House Diedne was a Mystery Cult? It could easily have been a Lineage or Societas. As the latter, it comes closer to having a common belief system, and magic to back that up. As the former, different knowledge based from parens to filius could explain their expertise.
But there wasn't such a requirement. Diedne Magic was, in fact, taught to Bonisagus (possibly only partially) because that's why hermetic magi have access to spontaneous magic.
They were secretive about their religious practices, and may well have had inner magic not shared with others outside the house, but that is not enough for a mystery cult as defined by the current rules system.
I did want to do a treatment of the Diedne that showed them having aspects of both lineage and mystery cult.
It was based on the some classic images of druids and ancient Briton/Celtic warrior castes. So you'd have those of a druidic background as keepers of both law and lore, while the more war-like magic from those who followed Diedne into the Order had their own take on things.
Within the house itself there were three lineages and while they each knew of the powers open to the others, they were not privy to their secrets.
In my story the Diedne were masters of their own downfall. The warlike path were up to no good. Not necessarily "diabolic" but they were certainly ambivalent about the code's proscriptions (for instance, Boudicca was an ancient practitioner of their arts, and her daughters didn't have to die for her to sacrifice them...). But the other two arms of the house, when confronted with the evidence by a quaesitor from within their own ranks, chose to silence the matter.
It's a bit of a tragedy really. Their secrecy and unity, in the face of the most obvious choice to renounce the rogue elements, resulted in the extinction of their house and their tradition.
Again, in my version, the strong spontaneous magic was a legacy from the war-like path who excelled at minor combat magic that swept their enemies before them. A little like the Verditius, they worked magic through tools, in this case a favoured weapon. When they joined the Order, they learned Magic Theory and this replaced the required focus.
It's a bit of a jumble as I never really explored it to any great degree.
I think they had secrecy because even in the final stages of the war there were no defectors. To me that implies that there is a taboo on their magic which does not allow them to share it with the uninitiated, even on pain of death.
And your standard of evidence is too high, if you think I'm going to tick every box for my prefered version. We know very little about them and so we are just guessing, that is, trying to see which model they lie closest to. I think there are indication of mystery cultishness, but I'm not going to be able to demonstrate it as defined by the current rule system, because Diedne have deliberately not been defined in the current rule system.
Magi with that background are required to have 'dark secret' as a part of it. A defector would be an open traitor to the house, teaching it's magic and turning on it in the war. This, plainly, didn't happen and I consider secret lineages with diedne magic exactly that, secret and keeping it that way or getting killed.
As for the origin of these secretive lineages, I think that is something that should be established for each story/game... but essentially I see the schism as a very chaotic and turbulent time, with a lot of magi being killed to say the least. It isn't inconcievable that during this time identity theft and thus secretly even changing houses could have occured.
A diedne member of a multi-house covenant could have had access to papers/communiques of another member to theoretically pull this off for example. Sure it is a big gamble/huge risk, but I think it could have been possible during that era. Most probably got caught, or ended up assassinating someone during the war and giving up the ruse to go fight or whatever. But it is an easy explanation for how the few covert lineages of hermetics with diedne magic could exist.
That's really up to us to decide when using the Diedne Magic virtue, yes? Any number of scenarios could describe this event.
The progenitor of a line of Diedne instructed magi in another house did break ranks and betray the house...
Prior to the Schism War, a Bonisagus magus claimed the apprentice of a Diedne who was already learned in that House's spontaneous casting abilities, and a line of Diedne Bonisagus descend from that character...
A Diedne maga joined another House, either by becoming part of its mystery cult (Bjornaer and Merinita seem best suited to this, but any would do), or by joining its societas. She never betrayed the secrets of House Diedne, but their teachings live on in her successors (forgotten by the rest of the Order) - perhaps this original maga even "switched houses" in order to become a spy...
During the Schism War, a magus of another House acts to preserve his personal friend by inducting him into that House...
After the Schism War, a Diedne survivor poses as a hedge wizard (concealing her preexisting knowledge of Hermetic Theory and Parma Magica), and successfully re-joins the Order through Ex Miscellanea...
A magus receives tutelage from the ghost of a fallen Diedne, bound to earth by its desire to resurrect the House...