How do you expect this to not be offensive? Drop the fake courtesy.
While we are laying out anecdotal evidence in support of our causes let me just say that when I got a job straight out of college I had better offers than most of my American classmates. I for one was not a cheap replacement for domestic labor.
Even if that were the case you can't talk about the broken H1B system without talking about the broken Green Card process. Give people an easy path to a GC and they have no reason to work below market wages. But if you simply do not want to complete with people who happen to not be born in your country then that's a different issue.