I can't say I understand this argument. Say an American company X outsources to a foreign company Y. Y abuses the system and hires a bunch of H1B and pays them

I can't say I understand this argument. Say an American company X outsources to a foreign company Y. Y abuses the system and hires a bunch of H1B and pays them pennies to the dollar. X is still paying Y dollars and not pennies right? Sure, the H1B is working for lower salary, but X's cost is still not a lot lower than hiring locally right? I see how just shipping the jobs to India/China might have the effect you are describing, but I don't think hiring H1B holders is the same thing.