This is just convoluted thinking, just like saying because it does not happen to every Apple device that it is not a software upgrade problem but a router problem!
I did not upgrade to 6.1.3 but I did upgrade to 6.1.2 on my ipad 4 and experienced similar wifi and bluetooth problems. I have home, office, restaurant and pub wifi networks that all necessitated manual registration to the network after the "upgrade". Does that mean all these wifi routers were faulty? I don't think so as my ipad now works flawlessly with all of them again!
I was put endless hours on the phone with apple support: reset network setting, software restore, factory reset all failed to solve the problem. I am not a technical person by any means but some of the suggestions from apple support staff verged on the ridiculous. After two days I eventually spoke to a guy called Brian who believed the issue was to do with the security settings in the wifi network settings resetting itself. At this point I was willing to give anything a try.
So I deleted my home wifi network, switched off the ipad and then added my home wifi network again with the security settings as none and then switched the ipad off again. When I switched on the ipad and it did not find my home network automatically, I was instructed to delete it again and choose the next option in security settings. We went through this process four times and eventually when we got to WPA2 in the security settings and I switched the ipad on again it automatically found my home wifi. It also suddenly started seeing all my neighbors wifi networks that it had not seen for days and bluetooth starting working too!!
Anyway this process is certainly worth a try for those experiencing problems with this latest upgrade. I really like my ipad, it fulfills all my computing needs and works without a hitch but I would rather not chance an upgrade to 6.1.3.
What is disappointing though, is that Apple, like the original poster I replied to, does not see this issue as their problem because it does not affect every user and every device. Instead of apple even contemplating the issue may be from their end and providing a solution, it is left to fixes like heating devices up or freezing it or blow drying it coming from user forums and to actually find something that will solve your problem is like searching for a needle in the haystack.
I was just lucky I suppose because after speaking to some poor customer service people I found a guy who went through every possible scenario to get the device working again. If you are reading this Brian congrats ona job well done and maybe you should head up the project team to sort this issue out once and for all.