The entire issue of what portion of private accounts people will and won't be able to pass on to their grandchildren is still somewhat vague. But the New York Times' Dan Rosenbaum and Robin Toner offer two telling details:

When workers retired, most would be required to use at least part of their accounts to buy from the government lifetime annuities, financial instruments that provide a guaranteed monthly payment for life but that expire at death. Despite Mr. Bush's declaration that money in the accounts could be passed on to children and grandchildren, the principal of an annuity cannot be inherited.

Money left over after the annuities were purchased would belong to retirees to spend or invest as they wished and could be bequeathed.

"Most" would be required to purchase annuities? From the description, it seems that high-income people who have other savings for retirement could simply pass on their entire private account when they retire, without purchasing annuities. Lower-income people who rely on Social Security for their retirement income, however, would probably put their entire private account into annuities (especially now that the yearly benefits will be smaller than ever). So in other words, the rich get richer, &tc. Brilliant! Now in fairness, lower-income families will be able to bequest their private accounts if they die before retirement. (In other words, throw momma off the train before she retires!) Perhaps lower-income people are more likely to die before retirement, I don't know. So that's good. But if that's the main or only appeal of Bush's privatization plan, then I'm deferring to Andrew Samwick for wry comment:

The issue of bequests is completely unnecessary. Social Security exists to provide insurance against outliving one's means. Nothing prevents people from leaving bequests currently if they so desire. I am not aware of any failures in the life insurance market that need government attention.

By the way, Professor Samwick makes another great point: it's ridiculous to think that politicians will never be able to take the money in these accounts away. Of course they can. They can raise income taxes on seniors. They can tax the disbursement. They can tax the fund managers handling these accounts, who then raise administrative fees. They can raise the price of annuities. Americans will "own" their private accounts in exactly the same way a little kid "owns" a ball in a playground full of bigger kids.