Since most of the problem mortgages involve people unable to make their payments, it can be safely assumed that the vast majority of them put down less than 20% down payment when they bought them.
I think a better way to help these people without destabilizing the market and costing the taxpayers a fortune, would be for the government to take over the PMI insurance business and drop the premiums for everybody's mortgage. This would immediately drop house payments from $100 to $400 per month. The risk would be less than the Feds are assuming with this program and would keep most of the people in their houses.
The other side of the fix would be to convert the ARM mortgages to fixed rate loans. I think these two corrections would stop the bleeding without a lot of risk on anyone's part.