Your characterisation isn't quite right. When Herodotus says "The people of Asia made no matter of the seizure of their women" he means they don't give a fuck about someone carrying off women. It's just this tit-for-tat thing that happens.

This comes at the end of a rather summarized history of Greek/Asian relations in the past. So these Phoenicians nab Io from Argos, then some Greeks grab Europa from Tyre, and then they grab Medea from Colchis. Her father asked for reparations, but never got any. Then Paris takes Hellen, and the Greeks FLIP THE FUCK out. They get this armada of a thousand ships and go BURN TROY TO THE GROUND! The Asians are over there like, "Dude, calm down! We didn't come smash up your flat when you took Medea!" That's the point Herodotus is making with this story.

He spells it out a little later:

Abducting young women, in [the Asians'] opinion, is not, indeed, a lawful act; but it is stupid after the event to make a fuss about avenging it. The only sensible thing to do is to take no notice; for it is obvious that no young woman allows herself to be abducted if she does not wish to be [Hello, Todd Atkin!]. The Asiatics, according to the Persians, took the seizure of the women lightly enough, but not so the Greeks: the Greeks, merely on account of a girl from Sparta, raised a big army, invaded Asia and destroyed the empire of Priam.

Given that you misconstrued Herodotus' point in your question, there's no way to say if that is reasonable.

Is Herodotus' claim that this is the version of Mediterranean history the Persians tell reasonable? I'd say it's a stretch to think the Persians are spending much time euhemerizing the Greek mythical past. I'm afraid I don't know a great deal about Achaemenid Persia. From the inscriptions and friezes I do know, it seems to have been more interested in promoting the position of the King (scenes of receiving gifts from subject peoples, etc) and promoting the Achaemenid religion, rather than dealing with Greek mythology. But I'm sure there's someone around here more familiar with Persian stuff than I.

Is the view Herodotus says the Persians hold reasonable? Today? ABSOLUTELY NOT! That thing about women only being abducted because they really want it is... well, colleges have mandatory classes about why that kind of claim is wrong.

Incidentally, the Greek word Herodotus uses for "abduct" here is ἁρπάζω, harpazo (like a harpy), cognate with the Latin rapio, or, in English, rape. It can mean any kind of taking by force, but it definitely includes rape.