As a student currently in one of Don's seminars at Harvard, it's important to note that the lack of assumptions in the nonparametric bootstrap (comparatively speaking) can also be viewed more as a weakness than a strength. That is, when one uses bootstrap to obtain confidence/credible intervals for a point estimate, the underlying model already makes a lot of assumptions on the data generating process. Therefore, it makes more sense that one use the same assumptions in order to construct a more accurate procedure for the interval estimates. Otherwise you're not using all the information you have. Moreover, if the modelling assumptions don't hold, then the bootstrap claims of proper coverage aren't going to hold anyways.
