Well, personally I'd guess:

- The player isn't used to the encounter yet, and thus worries (perhaps too much) about HP levels. I suppose you could add distrust of the co-healer here, and general inexperience.
- The player is one of those guys who think that keeping HP bars full is the mark of a great healer, the costs be damned.

Medica II is a quick and easy way to add a buffer for those groups of those people. No targetting required, just position yourself and let them HoTs fly (I do find that Medica II spammers are exceedingly bad at Regen, for some reason). Though I do cringe when I see a White Mage that never uses Assize or Medica instead, constantly overwriting their own Medica II hots. Or keeping it up on a fight like Faust where the only non-tank damage is sloppy add pickups or accidental cleaves. :/

As for Cure III... maybe some people don't realize that even with the Overcure proc, Cure III still has worse MP efficiency than all other single target healing spells?