...which is, I think, the way hedge fund managers only pay 15% tax on their $M income....
Let me address this one element of your post...
If you are a partner in a partnership (e.g., you are a partner in a hedge fund), you get a share of the income or the deductions generated by the partnership.
This is the key thing people don't understand: Those income and those deductions retain their character as they "pass through" to your return.
E.g., if you owned 50% of a partnership with a $10,000 charitable contribution deduction and a $100,000 long-term capital gain, you would get a $5,000 charitable contribution from the partnership and a $50,000 long-term capital gain from the partnership to put on your tax return. And these amounts get treated on your 1040 return in the usual way. Just as if you'd experienced them yourself.
So when do you get to pay at the 15% rate? That tax rate simply occurs when the income that's passed through is taxed on the individual's return at 15%... E.g., when the income is long-term capital gains taxed at 15%. Or qualified dividends.
In short, there's nothing magical going on here. It's just basic partnership accounting.
P.S. Hedge fund managers would not now pay a 15%... that's out of date. Their long-term capital gains rate would surely be 20%... and they'd also pay the 3.8% net investment income tax (aka Obamacare tax)... and then probably state income taxes too since they're in NY or CT or CA.