We can't prove it to be an either Or methodology.
Well, I guess it's just maybe imaginable that Rampires could reproduce their own kind biologically... but there's no evidence for it, and it doesn't seem to fit with how other supernatural types work.
The Red Court infection is IMO pretty clearly the RCV's version of the "scion/Choice" mechanic. All the "living" supernatural species - things with biologically alive bodies, not pure spirits or undead like ghosts, zombies, and Black Court Vampires - that we've seen enough of to know use that mechanic. Faerie and Changelings, White Court and the whole "first feeding" setup, Kincaid is apparently some kind of scion that made his Choice by his actions, even Foo and Temple Dogs (though admittedly it's not clear how the Choice works for them...)
(OK, wizards and werewolves don't work that way, but wizards aren't really a "supernatural species" -- according to GS anyone could theoretically learn magic. And werewolves are either specialized minor practitioners (Alpha-types) or people with a spell put on them (hexenwolves, loup-garou), thus just humans also.)
I guess it's just maybe imaginable that Arianna could have been the Red King's biological child pre-Rampire ... but even if that's the case she probably
also would have been his turning-child, because the Red King was the first Rampire and would have turned all the other early Rampires.
We don't even know the Red King was ever human. With what Odin says about 'mostly retired gods, the power of their blood spread among their descendants', I think it's at least as likely that the RK (and maybe the LoON as a whole?) were originally Nevernever beings who infected humans to create the Red Court as a species.
We know the spell was originally designed for humans and not specifically to target Ramps. It accepting a non standardized form of birthing, when as we know spells are made by intention and this particular ritual work done by the reds themselves, is all very suspect to 'plot device' to me.
Ah - but
whose intention? The Reds just accumulated energy (human sacrifices) and did the preparation, Harry finished the spell... I think Harry's intention was sufficient to change it to target a different kind of bloodline. IMO it's more or less equivalent to Harry redirecting the Outsider powered entropy curse at the Black Court vampire (falling turkey) in BR, except that in this case Harry was actually the one doing the final casting and so had more control.