Well then, you would be saying something factually incorrect, in terms of how D&D labels these things. A spell which heals can be either arcane or divine magic. D&D, in 3e, 4e, and now 5e, does not consider "healing" to be automatically divine. If you decide it is at your table, that's up to you, but the RAW is that healing is something that can be done without using "divine" magic.
By the definition I provided (which, apparently, is also in the Basic doc), the raw material is always the Weave, regardless of who is using it. So this "raw material" standard classifies divine and arcane magic the same way, at least in 5e. (I suspect 4e would be somewhat different, but 3e would be the same.)
See, again you are fiat declaring that a healing spell must, by definition, be divine. The books do not do that. Healing is healing no matter how it is accessed, and the method of access is determined by class. If you wish to view it differently, that's your prerogative, but that's not how the books are written.
Edit:
Additionally, I don't think it's a good idea for you to make blanket statements explicitly about "all editions," when you've admitted in this very thread that you have played very little of 3e and implied that you've played no 4e at all (again, I cannot assume you haven't, but since you didn't mention it the implication is there.) If it works the way you say it did in 1e or earlier, I'll have to take your word on that--I haven't played any of the "older" editions apart from B/X, and that was in an idiosyncratic but super cool custom setting anyway.