I don't see why there's a need to interpret this as a set phrase. It's just the standard use of という as hearsay ("They say [or someone said] that the way to do this is by...") followed by the explanatory/contextual の（だ）, then the conjunctive から. The difference between というから and というのだから is that the latter has a more strongly explanatory nuance.
(This is why learners are often encouraged not to overuse のだから in speech, as it came come off as unusually/uncomfortably forceful. If ちょっと急いでいるから is "I'm kinda in a hurry" 急いでいるんだから is closer to "Can't you see I'm in a hurry!?")
In this written example, obviously, this doesn't apply, and it simply serves to emphasize the reason for 士道's reaction. In this case, 士道 seems to find the idea a bit daunting, but I don't think there's anything in the use of というのだから itself that explicitly demands that the thing described be unexpected or surprising.
As for the link with the person describing it as a set phrase, I think the idea they were trying to convey is that there are cases where という doesn't literally carry the meaning of hearsay but is just more of a rhetorical flourish. In this case, however, it seems pretty clear that this is something 士道 has heard from someone else.
Yeah, I, either, don't think that's a set phrase. The meaning indeed can be "I don't fully agree with it, but~", but it differs depending on the context after all.
彼がそう言うのだから、多分そうなんだろう(I don't fully agree with it, but it would be so.)
彼がそう言うのだから、そうに違いない(I totally agree with it.)
As bentenmusume-san suggested, even キスをすることなので can have a similar nuance in your example.