If you dispatch it as a working fire it has a much different priority, response (emergency), and call reporting to it.
If you dispatch it as a PSC it's a much safer cold (routine) response and a much less dramatic procedure.
If you know what it is, what the extent of it is, and there's no immediate life or property safety danger, a PSC is a good code to use for it for those reasons. In this case, it really doesn't matter what terminology sounds better, it matters what call priority and risk the terminology brings. You don't want your situation response to be more dangerous than the situation to which you respond. (side note, this is something police have [rightly] gotten in very hot water for over the years, and now I hear burglaries in progress where a hot response isn't authorized because 'the caller can't hear the burglar at the moment')
I see your point, I just think Fire Alarm is making an accurate call on the risk of danger involved in the call and the corresponding response level to assign to it. Of course, if someone's on the phone screaming about a possible extension of the fire to an adjoining warehouse or home, that becomes a very different calculation.