I just had a Puppets' Bunker run with a co-healer like that. I sat on my lily stacks all the time, while he kept Medica II up and used Cure I to top off people all the time. Never saw an Asylum from him, and when I casted one he just overhealed it anyway. It's even more boring if all you press is Glare and a Dia here and there.

He even did DPS a little. At least I saw a couple of Glare casts whenever everyone's HP were full. So why overheal like crazy? Why even use Medica II after Plenary Indulgence + Afflatus Rapture?

Usually, when I use Assize as soon as it's up it at least tops people off. This run it was pure overheal all the time... I only used a few Rapture and Solace so that it doesn't look like I'm not healing at all, but only like 3-4 were even necessary when people didn't dodge AoEs.