That's a shame... as is the implementation of the AA itself. Why did they set it to be so aggressive? It's just painful to compare 360 screens with PS3 screens, sometimes. How could they not notice the blurring? How does FXAA cause this, anyway, when set to be so aggressive? I thought this post-process AA method was set only to target aliased edges, not to draw samples from the surrounding textures or add a full-screen blur filter.
Post-process-AA is applied to the final image so it doesn't know where are polygon edges and what are textures and tries to find the right edges just by anolysing the image to smooth the right ones. If it's too aggressive it will smooth everything that looks slightly in need of smoothing

I'm not sure why they did it, the PC suffers from the same problem but there you can just deactivate FXAA and use only traditional MSAA instead. Maybe they didn't know better, or didn't care about image quality

The FXAA looks fine to me, I think the texture quality issues stem from bad Ansitropic Filtering and Glowmapping. See how bad cave walls look when you're holding a torch - this problem was present in Oblivion too, even on the PC. The FXAA itself does a pretty good job of masking jaggies - much better than the X360 version. Look at the iron gratings outside Dragonsreach or any other semi-transparent texture and you'll notice the PS3 versions look much better.
I agree, the AA used in the 360 version isn't really good either. Some edges are nicely anti-aliased but it skips a lot with transparencies which gives the whole image an uneven look with smooth edges next to zero AA jagged edges. On the PS3 it's much more consistent and jaggies are less a problem.
But textures indeed suffer from the FXAA. In the comparison from digital foundry are some screens that show the problem:
http://images.eurogamer.net/2011/articles//a/1/4/2/0/9/8/5/360_aa.bmp.jpg
http://images.eurogamer.net/2011/articles//a/1/4/2/0/9/8/5/ps3_aa.bmp.jpg
Same texture quality just blurred on the PS3.
The same happens on the PC version if you enable FXAA.
http://images.eurogamer.net/2011/articles//a/1/4/2/0/9/8/5/pc_aa1.bmp.jpg
http://images.eurogamer.net/2011/articles//a/1/4/2/0/9/8/5/pc_aa2.bmp.jpg
or further down on this german page:
http://www.pcgameshardware.de/aid,854009/The-Elder-Scrolls-5-Skyrim-Tipps-fuer-optimale-Kantenglaettung-FXAA-und-mehr-Grafik-Detailstufen-im-Vergleich-Tipps-des-Tages/Rollenspiel-Adventure/Test/
nice for the otherwise aliased foliage but so much details lost and the ground just looks blurry...