Im pretty certain that Cleric spells that have a deities name by them are just most commonly used by Clerics of that deity but other Clerics can still learn and use them.
Deities also switch out some spel levels for their Clerics or offer a few nonCleric spells to their Clerics (like Sarenrae offers her Clerics Flame Blade @ 2nd) which only applies to Clerics of that deity, and unless specified does not apply to Oracles, Inquisitors, Druids, Paladins, etc. . .
I agree with Sean, but I also think other things that are written for specific faiths/races/etc should be exclusive to them rather than being open to everyone (like many of the options in the Advanced Race Guide; if they're for everyone, why are they placed in a specific race section?).
The infernal healing spell was originally written this way in the Asmodeus article in AP #29:
Level cleric 1, sorcerer/wizard 1 (Asmodeus)
Apparently the deity-name was removed when the spell was reprinted in The Inner Sea World Guide.
The fact that non-divine casters have access to the spell doesn't matter, since these articles originally said such spells could be cast by any priest who worshipped the deity in question. Priests can be of many classes, not only divine caster classes, as is also mentioned in several of these articles.