That isn’t accurate at all depending on your view of man in north america. Plenty of evidence has man living up and down the western coast of north and south america.
Topper, pedra furada sites are 30k bce. Monte verde 15k bce. All within the range of ancient extant equines.
I don’t think so. My recollection is that “horses” migrated ages ago at somewhere around the Mesochippus(?) stage. That was very, very long ago, probably before Homo sapiens existed.