There absolutely is no shortage. The distribution issue is taken out of the picture by looking at large firms like Google and Apple that can hire broadly. Google prides themselves on their interview system that has a high false negative rate. If there were any kind of shortage, they would probably be desperate to improve their hiring efficiencies. They are most definitely not concerned with that. On the other hand it is always in the buyers best interest to bitch about a "shortage" especially when they have regulatory influence. Why wouldn't they want to lobby for anything that can bring supply prices down? The day you see blog posts about Google or Facebook streamlining their interview processes (for both type I and II errors), I'll concede.
That, and there isn’t a shortage. There is a shortage of engineers willing to work for the wage being offered. When there is a shortage of a particular type of engineer, it’s because the company wants to pay $75,000 for a position that the market demands be $95,000. Thus the “shortage” and the “need” to bring in low cost H1 workers to fill that shortage.
Seems like if an engineer can easily hold out for 95k, it's because there is indeed a shortage that is big enough to do so. If there was a surplus of engineers instead, then more would be willing to work for lower pay, no?