No-one has ever seriously claimed that. It's self-evident that billionaires do not use a level of government service proportional to the amount of tax they pay, nor has that ever been expected or intended.
It can be as simple as understanding that, at the point that a single person or small group amasses more than a certain amount of wealth, that as a matter of course they have exploited the system under which they operate, and that it is better for the common good that they be taxed at a higher rate.
Or to quote a random Twit: "Once you reach a billion dollars, you get `I won Capitalism` trophy and your tax rate goes to 100%".
[citation needed]
No one seriously thinks "taxes are somehow proportional to the government services you use" at the individual level. The statement only applies at a societal level.
(But actually not at all, given how low capital gains rates are—being rich is a bargain of a deal)
You are confusing "service fees" with taxes. There are various tax regimes. Very few of them are proportional to the services you use.