Read it again. An independent corporation buys the house on behalf of the Muslims using a 30-year fixed-rate mortgage, and then leases it to them for 10 years. Their lease payments cover the cost of the interest on the mortgage, but they can tell themselves it's a rent-to-own situation.
Good God, there's no free lunch here. It's all spelled out in the article. Why do people believe that it would be any different? If Muslims decided their religion didn't let them pay taxes, the IRS would be on them like white on rice.
Correction: If Muslims decided that Allah or Mohammad didn't want them paying taxes, the ACLU would be all over the IRS.
OK, I'll tell you what, how about if you, as a presumable non Muslim, go out and try to find a good lease to own deal structured this way, that is arranged by Fannie Mae. Go for it. Tell me what you find!