Im not from one of the Big three and I also got invited by two Airlines for Assessment. I have to say, I am rated on B737 but no hrs on type.
PLUS I am already finished with initial training since 2013 and flew average 1 hr a year, namelijk keeping MEP IR current.
Also Ryan Air wanted to invite me, but since I am already rated and I am not willing to re do TR for another 30k nothing will happen there for me.