You don't have to pay AMT on capital gains, or dividends.
However, the lower rate might set off the AMT on your other income, depending on your mix of low-taxed income and regularly-income.
For example, if you had $1 million in capital gains, and made $200K in salary, you'd probably end up paying the 26% rate AMT on your salary, less the AMT allowance.
If, on the other hand, your income was the same but it was $600K capital gains, $600K salary, you wouldn't owe AMT because you're already paying more than 26% on your salary.
But the first example would still pay less overall income tax.