We're arguing at cross purposes here. There's several distinct parts to this and I don't think we actually disagree on most of them. Here are the key points as I see them:
- Arts can be granted by supernatural virtues in a general sense and this allows those without the gift to acquire arts. Some traditions already have the means to do so like the Learned Magicians, or Gruagachan.
- Arts can also be granted by opening the gift, in which case no virtues are required or granted - the gifted person simply gets all the arts directly.
- Not all traditions have developed these virtues in practice, such as Rune Magic or Hermetic Magic which practice only the opening of the gift as a means of acquiring the arts.
- For these traditions breakthroughs would be required to generate these virtues and the initiations to grant them.
I am not and have not been trying to argue that these virtues already exist in Mythic Europe in 1220, or that opening the gift grants these virtues (although as you'll see below I think it may be equivalent to granted free virtue equivalents). Only that these virtues can in theory exist, if someone discovers them.
We are in disagreement over the Hermetic Realm Integration, though. You're right that it's a context problem but not the way you suggest. If you actually read the result of the breakthrough it has nothing to do with allowing hermetic arts to be granted by virtue - that's just the example used because it's something so extreme to do with mystery initiations (it would inflict an excessive number of flaws and require a huge investment).
The result of the breakthrough is the following major virtue:
"The magus may initiate students into Virtues in the same way sahirs do, by convincing a spirit to accompany the student into the Magic Realm. This uses the character’s Rego Vim Lab Total instead of Solomonic Travel, and substitutes Magic Theory for Magic Lore, but otherwise works the same way: costing vis, reducing the spirit’s Might Score, and Warping the student."
The thing it allows magi to replicate is this:
"The process involves the teacher summoning a willing spirit to carry the student, in spirit form, into the Magic Realm. During the season, the student undergoes a sort of dream journey... The experience is very similar to what happens to Hermetic magi when they experience Twilight... While the student is in this state, his teacher performs the opening ritual and calculates his Opening Total. If this is 30 or more, the student gains a Major Virtue associated with the Art of Solomon that is also possessed by the teacher, usually a Solomonic or a summoning art. With a total of 25, he gains the Major Virtue but
also receives a Minor Flaw. With only 15, he gains the Major Virtue and a Major Flaw. These Flaws should be tied to the student’s travels in the Magic Realm"
There's more about the vis cost and the warping inflicted that I've left out for brevity, but that's the key part. This in no way allows for virtues that were previously impossible to exist, in fact it requires that the virtues already exist and that the person initiating has the virtue in question. All it does is give a way to impart supernatural virtues that costs vis and warping instead of inflicting other flaws (assuming the magus is skilled enough to not also inflict flaws).
The critical part is the bits saying things like "the student gains a ___Virtue associated with the Art of Solomon that is also possessed by the teacher". Sahirs have both gifted and non-gifted members. Just like with magi gifted members have their arts opened, and therefore do not gain the virtues but just get the arts directly - but they can still use this method to grant those virtues to ungifted people. The implication is that they do, in fact, have these virtues but that they are granted as free virtues when the arts are opened. There is no reason for this not to be true for the opening of the gift in other traditions as well, and the section of the breakthrough text "Soon powerful magi may even learn to teach Hermetic magic to the unGifted, by initiating them into each Art" supports this - any magus with this method and good enough lab totals could pass on the (currently unused but theoretically possible) virtues associated with the hermetic arts just as gifted sahirs pass on the virtues that they themselves don't explicitly possess. This is not inconsistent with the core rules - we know that arts act like supernatural abilities to an extent in regards to learning new supernatural abilities, so it stands to reason that this is because arts actually are like supernatural abilities but are simply free virtues granted all at once on the opening of the gift.