Warning: Spoiler! (Click to show)
Leather soles will wear out quicker in wet environments, but that doesn't preclude them from being worn in the rain. The sole will wear quicker because of the soft wet leather. You should be able to wear shoes a good bit in the rain before the soles wear out, unless you are walking very long distances on wet concrete. Even if he has been wearing them in the rain, what I see in those photos doesn't necessarily explain what's going on. Soles are lock stitched on, which means the threads are looped together in the stitch hole so that the threads don't separate even after the bottom is abraded by wear:
The depth of the loop or "lock" can be adjusted and is typically set to be 2/3 or so up into the hole from the bottom, so that the soles don't separate even when the part of the thread that is exposed to the ground gets worn away. Additionally, the exposed part of the thread is provided a little bit of protection by cutting a groove in the sole for the stitches to nest in. Also, the soles are cemented on before they are stitched, which can help keep things attached as well.
In his photos above, the stitch groove is still present, which means the stitches have worn away and separated before the lock stitch should have been compromised. This is unusual, and would be very frustrating. In other words, the "theory" behind stitched soles has failed in this instance. Does that mean that AE or Nordstrom has to do something about it? Not necessarily, since it is pretty much impossible to prove that they have only been worn a few times, and that they weren't abused (like plucking the stitches out from the top). It almost looks like the thread has been pulled, in a similar way that you can pull a thread on an article of clothing, which can start a domino effect of unraveling. However, that's impossible with a lock stitch. I'm not saying that the OP has done this. I'm simply saying that this is unusual. I won't be surprised if they take the shoes back or repair them at no cost, since both companies are known for stellar customer service. If it has been a completely natural occurrence, I would personally classify it as a defect, and keep my fingers crossed that they'll fix it or exchange it.
Don't expect this to happen to your shoes simply from wearing them in the rain though.
Great response $$