I’m fascinated. Could you go into more detail, maybe give an example?
The AMT deduction for 2012 is around $33,000 for a single filer. The standard deduction for a single filer in 2012 is $5,950. So anyone who has lots of itemized deductions that exceed $5,950 (mortgage interest and state/local taxes, for example) under their normal tax bracket, the AMT deduction may actually exceed these by a wide margin.
Keep in mind that nobody "saves" taxes under the AMT. Each taxpayer is required to do a separate calculation to see if they owe more under the AMT or under their normal tax bracket, and they pay the higher amount. But if you do end up paying the AMT, you have a huge incentive to change your financial circumstances because you lose out on those itemized deductions anyway.
As an FYI ... this is exactly what precipitated the collapse of the housing market in California in 2007 -- more than a year before it rippled across the entire U.S. Astute financial advisors were telling their high-income clients in California to sell their homes and either rent instead, or move somewhere else. Once these people ended up in the AMT bracket, they lost their deductions for mortgage interest (on expensive homes) and state/local taxes (which are ridiculously high in California).