SkyWest-operated flights should credit to AAdvantage without difficulty as they are AS flights. Just like Horizon, SkyWest (OO) is operating as a regional contractor for AS, so you are flying on Alaska Airlines Flight XXXX, proudly operated by SkyWest. Your question is question is very similar to that of AS Mileage Plan Members who ask if they can earn miles on Delta flights operated by Delta Connection carriers, which they can.

What gets confusing is that AS.com will display flights as the operating carrier's flights despite them being codeshares. This means that AS will show flights where SkyWest is operating as Alaska Airlines as SkyWest Flight XXXX and will also show flights where SkyWest is operating as Delta Connection as SkyWest Flight XXXX. In the latter situation, you would not earn miles as it is not an Alaska flight, even if AS will codeshare on that flight.

IIRC, there was a period when AS/QX employees could not travel NRSA on Skywest-operated AS flights, but that is the only difference I've heard about.