I would not agree that this is an absolute. Just like "needing" a $50,000 wheelchair when a $200 set of crutches would do, what a person needs in the way of mental needs is very subjective. That's some of the reason doctors write prescriptions, to verify the level of need meets or exceeds some standard. In some cases, a psychiatrist may need to give a nod to a mental need if you want insurance to pay for it.
Diapers are an interesting issue because they have a plain, obvious, well-known assistance to a physical (/medical) need, as well as a less known but still not terribly uncommon mental need. I think misrepresenting your need to "game" the system isn't honest. If your need is mental rather than physical, represent it as such. If they allow it, ok. If not, use your own nickel. Insurance is for a specific thing, for a specific reason.