Most GPUs does adjust MIP LOD levels when applying AF but this doesn't lead to anything like more bandwidth usage or more memory needed. You're still using the same base texture and the same number of MIP levels.
You have the same base texture and the same number of MIP levels, but that doesn't mean that you're actually sending them to the GPU to be sampled. If a GPU decides that it only needs texels from MIP3 during trilinear because of the distance and oblique angle a surface is at, it's not going to bother reading in stuff from MIP2, MIP1, and MIP0.
Also trying to tie MIPs into this conversation is rather pointless because MIPs are generated on the GPU on the fly these days - in pretty much the same way as AF.
If this is true, then this is where my mistake lies. Obviously my claim that AF could increase BW for oblique-angled surfaces relies on the idea that the GPU would actually read in smaller versions of textures in trilinear cases.
I was under the impression that MIPmaps still resided as actual textures in main memory, and that the GPU would still only draw from the required MIP level to minimize cache thrashing (and consequently, BW). I got this notion because AMD's own commentary about GCN suggests it,
such as this compilation of tweets, or
these slides from their 2014 developer conference, in addition to everything else I've seen about modern texturing methods. If I'm wrong about this, I'd like to see something that suggests otherwise.
Obviously GPUs are very capable of generating MIP levels due to their excellent scaling abilities (and shaders being an alright fit for texture compression algorithms), but I thought that was mostly used for loading (i.e. as textures are read from disc) and for procedural purposes, and that texture sampling still used classical MIPmapping. After all, ditching classical main-RAM mipmapping would require excessive BW for any objects where the texel density exceeds the on-screen pixel density, since you'd have to read in all those subpixel texels to supersample away the texture aliasing. Considering that a lot of modern GPU tasks are BW-bound and that there's frequently a decent amount of RAM to go around, this seems like a terrible idea versus just eating the extra 1/3rd memory cost on MIPmaps.
AF doesn't have anything to do with MIP levels. AF is a tap filter which does supersampling when fetching texels.
...Which still requires MIPmapping to get stable results, in exactly the same way that bilinear/trilinear does. 2 taps allows you to use a slightly bigger MIP level, hence why it pushes the "blur" region back a little. If you tried to use 2 taps on a full-res texture for a highly-oblique surface, you wouldn't get blur, you'd get a ton of texture aliasing.
AF isn't MIPmapping, but the concept relies on MIPmapping in exactly the same way that other texture-filtering techniques do.
