No, the person proposing the progressive tax is simply saying that there is an optimal, non-zero level of taxation that creates the best outcome for society as a whole. This person could be at the top or bottom bracket with no effect on the argument. The richest in our society actually generally agree with that notion, cf. Gates, Buffett, as well as those who have the most to "gain" directly through distribution of public services.
And yes, even though it wasn't my point to begin with, it is possible to distinguish ideologies in the case of wanting higher taxes vs in the case of wanting lower taxes by outcome. In the case of wanting lower taxes, without regard to ideology, both payers would want the taxes on themselves to tend to zero. In the case of higher taxes, the ideologies do differ by outcome in that the ideological party will want to pay something herself, whereas the disgruntled party would have to impose taxes on "the rich" and not on themselves (relatively) to achieve a desirable outcome (this assumes they don't "hate" themselves as well).