The question moves from two observations— that among industrialized nations, the United States spending on philanthropy is the highest (1.67%) and that its taxes on high-income individuals are among the lowest— to a speculation about the thought process of donors. Hmm, well.
There have been a number of studies on the effects of income tax rate changes on charitable giving. According to a 2008 paper by National Bureau of Economic Research researchers entitled How Does Charitable Giving Respond to Incentives and Income? Dynamic Panel Estimates Accounting for Predictable Changes in Taxation, charitable donations among the wealthy are relatively inelastic. Tax rate changes are seen as short-term fluctuations, whereas the level of philanthropic giving is governed by long-term considerations, and so the result is in line with Milton Friedman's Permanent Income Hypothesis.
For very wealthy individuals, tax benefits are not in and of themselves a reason to start or to increase giving. Even though the U.S. has strong tax incentives for charitable contributions, federal income taxes started falling 1981 and are now among the lowest in the industrialized world. Donations have thus become more "expensive," yet against predictions, giving has actually increased. As The Economist notes, "Surveys suggest that tax rules affect the size and timing of gifts, but not the initial decision to give."
I must include some comments on some other possible misapprehensions. First, a feature of American philanthropy is that it is considered a civic duty of all classes, not just the wealthy, as attested to by de Tocqueville (and by universities' aggressive solicitation of donations from their deeply indebted recent graduates). Second, it is arguable that philanthropy affects the tax code as much as the tax code affects philanthropy. There is broad popular support for the role of non-profit organizations in American society and genuine concern when their funding is imperiled. Indeed, the tax deduction for charitable donations was actually introduced during World War I out of concern that high taxes would make Americans less generous to their churches and hospitals. Third, philanthropy is tied up with social and religious sentiments which can trump purely economic considerations. The Economist article linked earlier notes that France has much stronger incentives for giving than Germany, yet Germans give substantially more as a percentage of GDP than the French.
There are whole think tanks that study the role of philanthropy in American society who can probably provide a more authoritative answer. Some recent histories on this topic include Charity, Philanthropy, and Civility in American History by Lawrence J. Friedman and Mark D. McGarvie (2002, University of Cambridge) and Philanthropy in America: A History by Olivier Zunz (2011, Princeton University). The seminal work was American Philanthropy by Robert H. Bremner (1960, rev. 1988, University of Chicago).