Since there are two distinct asertions in my post, I wonder to which of them you yourself in your own work have found different conclusion.
I have 27 years in the chip design industry as an ASIC design engineer / Manager (EE). I have worked with H1B's for many of those years at National Semiconductor, Motorola, Synopsys, Teradyne, Intel and lots of them at my new company. I've not know any H1B's that were paid less than there indiginous counter-parts. being a manager ... I AM privy to the pay scales