I suppose it wouldn't completely surprise me to see a regional doing this. However, it's a big leap from requiring "...the legal right to work in the United States..." [or words to that effect], which most carriers including the big legacies state under requirements, to a company actively recruiting overseas and sponsoring people for visas.
I don't see any statement about sponsorship on Skywest's website. Have you seen it stated in some official place ? It would be a new twist on events here and worthy of a good bit of publicity.