I'm 80% certain it isn't a shared pool. There have been countless times I've dumped 60 gold rerolling for a champ that literally only one other person has just 2 of, and get nothing. And this was after everyone had slurped up a ton of 1-star champs, so the "pool" should have been extra small and almost entirely fully stocked with the champion I was looking for...
This is not a rare occurrence. If it happened a couple times, I would say "RNG does that". But when it happens with regularity to a severity that should happen only 1/100, something is going on that they're not telling us. Either it's not a shared pool, or there is rigging behind the scenes that they're keeping a secret. Either way, it feels bad.