I just read through this topic out of curiosity, being a former message board admin. I was finding it difficult to believe anyone could log into 10+ accounts and vote in a poll within roughly a minute.
If the assertion above is accurate (alphabetical order, old accounts with very few or zero posts), it sounds very much like a programmed script that searched through the database by username, checking post counts and dates, logging in (perhaps even altering the password), registering a vote, then blanking out the IP.
My experience is with phpBB, but unless vBulletin is that lax, I don't see it accepting any actions without an IP address. If I understand correctly, even proxy sites have an IP. They just mask your originating IP with their's.
It would require intimate knowledge of vBulletin and it's password encryption algorithm (assuming it uses one).
Just my $.02.