Hey all!
For clarity, items and their stats are determined at the time that they're generated in the game world. In most situations, this is when the item physically drops (like from a monster, a chest, or a destructible). In cases where there isn't a physical drop, items and their stats are determined as soon the game creates them. For example, items from Kadala are generated as soon as they're purchased. Item types, stats, drops rates, etc. are not determined, or pre-determined, upon creation of a character nor is that kind of information stored in some sort of seed on the character itself.
It's important to keep in mind that random != uniform or equal distribution. It's completely natural for random systems to included clusters, and for the human brain to interpret those clusters as patterns (even where there are none).
Thanks for the discussion, though! Theories like this are always interesting, and of course can yield great feedback on and insight into potential related issues.
I'm going to go ahead and lock this thread up, though, since the theory isn't actually accurate and I'd like to help curb some of the misinformation.
In parting, for your trouble, I'll leave you with this:
Heads - YouTube