That said there are many things which Blizzard could use to connect your account (and no, IP address won't be one of them)
This is simply not true, Wolfpack. There are several reports, lost in time and space, like my own, where the IP address was used to connect several computers and all accounts.
Yes, it might have to do with selling gold; but it was indeed used and confirmed by Blizzard GM (of course, believing what they say is up to every person.)
In the end, best approach could be avoiding to consider Blizzard as stupid folks. They had all our asses twice in the last 7 months, but we still try to flag them as incompetent and unable to properly do their job.
What do I mean? Well.....they do have the IP address info, that's a fact. They know when several accounts are using the same IP at a given time, as proven by direct conversations with GM's many times before.
They have the info, it is the cheaper and less resource consuming legal way to find botters, except soft detection.
But somehow we decided they can't use this info to flag accounts based on a 1 per 1000 case that the IP is a shared one (college, residence, whatever...)
I think we have chosen to believe it because it creates a false sense of security for us. ("They can't do that, thankfully...") Heck, not autobanning, flagging accounts for manual investigation.
Reality is that flagging offending IP's is a very efficient way to catch botters; there's a reason other games still use that info to do so. (PoE, GW2, FFXiV...)
There are many other ways, and this last banwave sadly sounds a lot like software detection, which is the worst possible outcome.
But stating that they don't connect accounts on IP as you did, is wrong and misleading. They aren't dumb, they have the info, yet they don't use it out of a 1/10k chance of error. Not very smart.