Every peer makes an announcement that they've seen a new transaction to every one of it's 8+ peers, if a peer doesn't know about the transaction that's announce

Every peer makes an announcement that they've seen a new transaction to every one of it's 8+ peers, if a peer doesn't know about the transaction that's announced, they send back an inventory request to get it for themselves. There's never really many degrees of separation between nodes, but you're probably incorrect in that blockchain.info knows anything about the originator of the transaction. They connect to a large number (abusively) of nodes, but not enough to do this sort of discovery. There's a reasonable portion that never expose themselves to the public network at all.