I think so. The fact that skilled immigrants actually are skilled probably helps the notion that skilled immigrants don't need help and doesn't deserve any sympathy.
On the other hand, skilled immigrants often seem completely oblivious to the fact that they are completely being discriminated against. Just like blacks who thinks they are being mistreated simply because of their skin color at birth, and women to their gender at birth, skilled immigrants can perfectly adopt their narrative of mistreatment due to birth location. And yet, they don't. They simply take the world for what it is, and try to win it based on merits. Maybe it's because skilled workers go beyond race and gender, they themselves have a hard time identifying themselves with each others.