Imagine we had a really Spicky ball, or a giant see urchin, with some spines coming right up to our eye and the center of the spiky ball/see urchin being somewhat far away (so we use a high mipmap level). And this shape was covered with a repetive texture, like checkerboard. Would it look good with trilinear filtering? Or would there be a harsh cutoff somewhere from checkerboard to gray.
To answer my own question (from watching more of the lecture and hearing Kevin's helpful answer) - this would look bad because of the averaging and the sea urchin/ball would just look gray in the middle. Anisotropic filtering is the fix.