That may be driver-dependent, but I've never seen NEAREST_MIPMAP_LINEAR getting anisotropic filtered.
The _MIPMAP_LINEAR thing, afaik, basically tells the GPU to use linear filtering when generating the mipmaps. So, it influences the quality of the data that's rendered, but not the rendering itself.
If you're noticing a difference when _MIPMAP_LINEAR is turned on, your GPU may be generating anisotropic mipmaps (ripmaps) for the textures. But I'm still skeptical about it using anisotropic filtering per se.
Anisotropic filtering is like a superset of trilinear filtering. While trilinear filtering filters across square mipmap levels (both coordinates at once), anisotropic filtering filters across each texel coordinate individually.
Now, the huge catch is, pretty much all GPUs requires bilinear filtering to be enabled if you want to use trilinear filtering (and anisotropic filtering)... But mathematically, bilinear filtering isn't required. Bilinear filtering only filters across the UV plane, regardless of mipmap level. You can still blend mipmap levels (including anisotropic ones) without blending UV coordinates.
Well, this video
doesn't show it, but Retroquad can do trilinear filtering of mipmap levels without doing bilinear filtering of texel coordinates.
I also want to implement anisotropic mipmapping someday, and it won't require bilinear filtering either, but anisotropic filtering may require it. Anisotropic mipmaps can be trilinearly interpolated across mipmap levels with the same width/height aspect, but afaik, to do anisotropic interpolation on them, the blending across mipmap levels must be done in a subtexel scale. Or maybe not. I haven't got to that part yet.