Well, I think overall the same basic debate ensues. The first issue IMHO is the higher bar for fictionally justifying it. Everyone is likely, in a god run world, to have SOME sort of relationship with the gods, and they have a history of healing magic, so there's a fairly ready-made fictional position there to exploit. What about this more 'arcane' sort of magic, which is generally getting explained as being a result of deep practice and theoretical and practical understanding of some sort of 'laws of magic'? It seems a LOT less easy to justify the notion that some random fighter, having nothing in her background to indicate otherwise, is sufficiently familiar with these laws as to provide them with a chance to replicate the casting of a complex level 3 spell.
I mean, go ahead, as the player provide your justification in the fiction. I suspect we're all going to pretty much agree that this is going to have to be pretty good! OTOH apprentices are able to carry out cantrips pretty reliably, so perhaps a fighter with really good fictional justification and some real luck/skill might pull off something similar one time. The consequences of poor die rolls I leave to the imagination, but they might not be all that pretty!