Is it? Sure, if you start with "we have domesticated horses, how did we get here" then "one event happened" are less assumptions than "two events happened". But if you start the other way around with "humans lived in vicinity of a species that lends itself to domestication" then "they only domesticated it once" sounds like the wild speculation.
Even if you assume exchange between the two civilizations, spreading the idea that horses can be domesticated is much easier and lower friction than spreading actual domesticated horses. Especially with a mountain range involved and early generations of barely-domesticated horses.