The jobs overseas are *already* much cheaper than what the H1B's are getting paid. If it were possible to have these jobs overseas ---they would already be there---, and that is cold hard fact. The jobs going to H1B are jobs that require face-to-face interaction with people here in the United States.
The 'alternate fact' here is the obvious bluff from tech companies (Let us play by our rules or we'll ship jobs overseas). The only response that has any integrity is "Well, take your goddamn ball and GO home then."