I am not convinced there are two separate areas of knowledge.
(Mystery Cult) Lore is the (Organization) Lore of a particular cult. It provides knowledge of the legends, history, structure, operation, and goals of the Mystery Cult in question. It includes knowledge of the magics, rites, and secret passwords and symbolism of the cult, how to covertly signal membership, and how to assess another magus’s membership or non-membership in the cult. [TMRE:11]
It may not be possible to separate an understanding of the organisation of the cult from the teachings of the cult, and hence every mystery cult lore is just the organisation lore of said cult.
Taking Tremere Lore as a mystery cult lore, and let the house provide initiations does not seem categorically wrong. I just did not have the impression that that would be how the house operates. Inventing a Tremere Cult Lore would be no less misplaced.
Of course, if the saga is overly liberal in the availability of cult membership and initiation, and exaggerates the antagonism against Tremere, you are right that something has to be done to level the playing field. Personally, I would make cults rare (most canon cults do not exist), and members have to ask themselves what they can do for the cult, rather than what the cult can do for them. TANSTAFL
If you find that Tremere is disadvantaged and you have no other way to mitigate, making a Tremere Cult may very well be a lesser evil. However, you could consider their having a bargain with a faerie queen able to bestow certain virtues. That is probably the same thing, though, with some narrative sugar on top.
Actually, it easily becomes a challenge for the entire troupe and the SG in particular, not just the deluded players.