Depends a lot on the nature of magic in your game world. In Forgotten realms, divine and arcane both come from the same source (the "Weave" or Mystra). There are several examples of "healing" arcane spells there as well (albiet very high lvl and very limiting).
There really is no concrete explination out there. I think that the deciding factor is really just to distinguish the clerics and limit the wizards (game balance type thing).
Personally, I would allow a spectral hand to deliver a healing at range in my campaign. I don't think it is a problem. And by the rules, there really isn't anything preventing it that I know of. You could not, however, sacrifice a magic missile for a healing spell across classes.
TLG