El Mahdi
Muad'Dib of the Anauroch
Absolutely.
When hp loss represents wounds in the narrative, healing herbs can heal wounds. Especially because herbs can be in that "supernatural" space quite comfortably (you don't need to be a spellcaster to use one, but they might have some magical properties of their own). But "strictly Charles Atlas-style inspiration" can't heal wounds, and I don't think it's claimed that it can. So it's not compatible with hp loss representing wounds. Contrast, say, bardic healing, which can fit a sort of "magically inspiring" narrative - that can heal wounds just fine.
For clarification purposes, and please correct me if I'm wrong, you're saying that healing potions support a non-magical game even when you describe them as "supernatural", the link you posted to describes them as "magical antidotes", and the PHB itself says:
Potion of Healing
A character who drinks the magical red fluid in this vial regains 2d4+2 hit points...
...do I have that right?
Inspirational healing works fine if you let it be supernatural, OR if you make HP not about wounds.
This may be your perception or preference, but this is objectively incorrect. One can deny it as much as desired, but I and others have shown over and over how it's consistent with the rules as written, and consistent with real-life - both with no magic required.
There's really no getting around that, no matter how many times this sentiment is stated.