Perhaps it is a myth with no basis. That said, increased supply decreasing demand is usually the null case, yes? So I'd want to see evidence that additional workers do not supress wages.
I am not purporting that the H-1B program has no effect on tech wages, just that it has a negligible effect due to its small cap relative to the number of tech jobs available.
Any increase in labor supply would have some effect on the wage level in an industry.