If you have more people competing for the same job, then the wages go down, and vice-versa, the less potential employees you have, the higher the wages have to go to fill the position.

The supply/demands fraction is basic math. Are you saying math doesn't work?

That statement is pretty vague and pretty obvious on some levels but provides no concrete numbers and evidence that's generally applicable (basically it's easy to cherry pick some results and make generic claims afterwards that don't hold water).

I'm not pro-immigration and I'm not anti-immigration but I know math and personally experienced that whenever you have a lower supply of candidates then I have much more leverage for negotiations and better work conditions and have experienced the opposite, of employers being dicks due to over-supply of labor.

I therefore take those "research" findings with a generous train load of salt.

edit: sorry, just seen your edit. Care to elaborate why you think they are dismissible?