MachOverSpeed - The rules this side of the pond are simple - UK airlines can lease in foreign registered aircraft for six months then they are supposed to go onto the UK register (unless there is some overwhelming reason not to do so). There is also a very strict limit on the proportion of foreign to UK registered aircraft that can be operated.
Atlas therefore had/has to set up a UK operation - which is then required to obey the various regulations (employment, licencing, etc) in force - which means that UK/EU nationals get employed in preference to non UK/EU nationals - same as you have in the States.
Getting an aircraft on the UK register is not an easy thing - it's very expensive and time consuming. If the Atlas crew member's paranoid fantasies were in any way true, then Atlas would not only have to reregister all their aircraft in the UK; but they would also have to have sufficient crews here to operate them as I'd assume you guys would all be on strike, wouldn't you?
So, unless AACS has say 100 fully typed and current crews just hanging around twiddling their thumbs, it isn't going to happen. This deal is strictly for BA - and to suggest anything else is laughable!!
Moving on - if the pilots to which you allude were 'sponsored' then they weren't illegal, then, were they?
Petergozinya - why on earth would I want a green card if I had to deal with people like you on a regular basis?

- it's bad enough that you Yanks think that Paris is in Texas; Reading is in Pennsylvania and Newark is in New Jersey!
At least when we have an election it's free, fair, equitable and we know who wins....