Romney has now been quoted as saying that he has "never paid less than 13%" in taxes, by which he presumably means federal income taxes. Unfortunately, this statement is meaningless, because of the question: 13% of what?
Suppose that in a given year he got $20 million in capital gains from Bain carried interest payouts and such, and had $3 million in ordinary income (from fees, interest, dividends, etcetera). But suppose further that he deducted $2 million in fake ordinary (i.e., not capital) losses from tax shelter transactions, along with $19 million in capital losses from "strategic trading / loss harvesting" (the sale of down stocks from his portfolio, while he continued to hold the appreciated stocks), as well as from additional tax shelters that created fake (not merely selectively realized) capital losses.
His adjusted gross income (AGI) would be $2 million - not $23 million, even if the higher amount was a more accurate representation of his economic income for the year. And with this being half ordinary income, half capital gains, he could well end up paying 13% or higher, even with itemized deductions to create taxable income that was less than his AGI.
Suppose he ended up paying $300,000 of taxes. This would satisfy his 13% claim even if we assume that he is using AGI, not taxable income, as the denominator. But if we compared the taxes paid to the full $23 million that he really earned for the year (even not counting unrealized asset appreciation that the tax system generally ignores), it would come out to not much over 1%.
In short, even if Romney is technically telling the truth here, there is absolutely no reason to believe that his claim has any meaningful content.