Yes, her AMT hit is a clue that she's gaming the system. I doubt that it reflects oil and gas from her own property, as she'll get a "depletion allowance" for a lot of that income that offsets the real profits.
Not claiming any foreign tax credit, however, is a big clue that she is filing foreign tax returns and paying taxes overseas on her income (i.e. owing taxes over there rather than being due a refund) where she no doubt has a better deal negotiated than here. Thus, her two currently released pages subtley suggest that she's using Benedict Arnold loopholes.
The kicker here, however, is that this is all play money. Whatever taxes she pays right now while she's in the public eye (at least partially), she can get back by filing an amended return in the next 3 years.
In the meantime, she simply loans Uncle Sam the amount of her AMT hit. If she wants it back, there are no doubt accountants who cant get it back for her.
Also, the bigger picture may be that her wealth is almost entirely sheltered in trusts. Either Mrs. Heinz-Kerry or her trusts took a bath when Enron went bankrupt, for instance. No doubt they have losses that still "carry forward" to reduce their current tax burden. Her accountants can pick and choose when they want to apply those losses, as political or financial matters dictate.
We've got CPA's here on FR. They need to itemize the potential back-dealings that could be in play here.