Employers can bluster all they want; in the end, either they need to be happy hiring someone willing to work for the wages offered, increasing the wages offered and spending a lot more time looking (better wages gets you access to a larger pool, but it in no way chases away the incompetent, you still need to filter) or doing without the employee. As an interviewing worker, this means that you don't need to outrun the bear; you just need to be better than nothing, and better than anyone else willing to work for the same position. I've been working since '95 or'96, and personally don't feel I've actually been qualified to do any job I've had... but I'm better than nothing, and beating the competition is usually not very challenging.
As far as I can tell, the facts on the ground for contract work (which is to say, lower total comp than working as a FTE at one of the local big companies, lower job security, less respect, and generally slightly worse working conditions) means that when you are hiring contractors for a big company, you are hiring from a pool of people who are unable to get the same job at the same sort of company as a FTE.