I have had success in tourneys where I was only 4 or 5 times the Big Bet and still hung around for a good hand. I have even been as low as to barely have enough to feed the blinds and antes to make it to the next round and made a come back.
Not saying this is the best strategy. But, if I pushed in every time I got down to 10x the BB I would be out before I even hit the money the majority of the time I play.
I think the name of the game is survival because you never know when you are going to lose to total trash. That volatility is to much to overcome if you push with as much as 10x the Big Bet. Think about being short stacked at only 50/100 blinds and having 1000 left of 1500. That can happen often.
If I get a marginal hand I am not going to push in there and hope.
It is hard enough at that level with the crazies that are still left to win with a good hand. Let alone pushing in with almost anything and praying.
Like I said. I am refering to Freerolls.
In a real tourney you might get QJ off make a big raise and will see only good hands stick with you. You are likely to win the hand outright preflop.
So, 10x the Big Bet is likely a very good number for real tournies.
For freerolls. I would will wait for a really good hand before I commit my chips.
Given the choice between being knocked out playing a marginal or junk hand against a junk hand and being in the Money. I will take being in the money and scratching my way to the final table anyday.