Assume for the sake of argument that all 21 million coins were in circulation as of just today. Suppose some rich reputable entity (Bill Gates or the Pope) bought up all bitcoins at market price (29 cents) for $6,090,000.
I have a bitcoin, I'm not selling it at 29 cents. How is anyone going to get them all for 29 cents each?
And this really has nothing to do with me thinking that the market price is really low right now. If coins went to a billion dollars each I'd still have no reason to part with my last one since I'd have more than a trillion dollars already.
You can back stickers with platinum if you want, but 'backing' is only as good as the word of the backer.