The US Regionals are positively overrun with (mostly european) expats. Seriously, flying in to Memphis during the Pinnacle push sounds like you're in Brussels. I assure you there's a way to do it, and it can't be that hard because every Tom, Dick, and Jacques is doing it.
This is very misleading information you just posted. I worked at Pinnacle for six years and yes, there are a LOT of Europeans, Africans, Asians and everything under the sun working there. But I can assure you that every single person working there has the right to work legally in the United States. I recommended a good friend of mine to work there after I had left and he did get the interview and the job offer with the condition that he presented his "permanent" residence alien card, my friend had just received his green card but it was the temporary certificate that they give you until the permanent one arrives on the mail.
Pinnacle would not assign him a class date until the permanent card arrived on the mail and that caused him to get in a later class date.
Also the aviation field is not one of the careers listed for the application of residence visas by professionals that is currently flooding the medical field in the US with doctors and nurses from other countries (specially India and the middle east) The INS does NOT consider aviation to comply with the requirement to issue such visas because there is no lack of supply of domestic pilots (lack of experienced pilots perhaps, but not a lack of supply)
As it stands right now, there is NO way to obtain a job in the aviation field in the United States without having legal right to work and reside there.
Sorry