One does not need to be a strict economic determinist to see the connection between one's sources of income and one's political interests. Most of those that see transfer payments as too high, for example, are likely not receiving them.
Although the claim of class warfare is pinned to the left, the elites are, arguably, even more class conscious. Aspirations to advance to higher quintiles may also impact how one perceives distributional and other issues.
The study accepts the general orthodoxy about transfer payments. Consider that the gains on the return to capital (profits, interest, dividends) are taxed at a lower rate than the returns to labor (wages and benefits). This, and tax breaks for businesses, should arguably count as transfer payments as well. Tariffs on imports are also transfer payments. The way transfer payments are understood in the study is itself very much pregnant with ideological assumptions.