This is not always true, for a couple of reasons:
1) If you got that H1-B by way of Infosys or Tata (as opposed to getting it straight from the US company), the dynamics are radically different than what you state, and those two companies alone make up an almost-majority of visa-holders (how that happened? 'hell if I know.)
2) Your statement only applies to those workers who are sufficiently competent in the field they work in, which is, sadly, only a fraction of the total (mind you, this is the case in any given group of people in any given field, so don't take it as a snipe against foreign workers specifically). I say this because you still have to demonstrate the competence at an interview. It is one thing to get recruiter offers, but another entirely when you have to sit in the interview.