The Vanguard Group is a mutual fund company whose adviser is owned by the funds, rather than being an independent profit-seeking corporation, so it can charge its funds lower advisory fees than its competitors do. (Disclosure: I am a Vanguard investor.) But the adviser is a taxable corporation, while the funds themselves are not taxable (they just pass through taxes to investors). There is a theory that the adviser should be charging Vanguard higher management fees, to reflect the "arm's length" prices that an independent adviser would charge, rather than the "at-cost" prices that it does in fact charge. Or rather, there is a theory that Vanguard owes taxes on the fees that the adviser should have charged, which would have been profit to the taxable corporation.
Why is there any fee that "should" be charged? The premise seems flawed that fees need to anything more than cover costs to pay the employees to do their work.
"If this structure were different, they'd charge more and make a profit and pay tax" ... But it's not different, so it doesn't make a profit, so it doesn't pay tax. Pretty simple.