You can’t really refute the claim that H-1B drives down the market price of labor by citing their price in the market. You have to show those wages would be the same even without the immigrant workers. From a basic supply and demand perspective that sounds unlikely, but markets are complex dynamic creatures so perhaps it’s the case. Nevertheless it needs to be shown.
Agreed, markets are complex. And frankly I don't find market based arguments for or against immigration particularly compelling for that reason. So far as I can tell we really have no reason to believe either side's claims along that dimension.