Not true.

"Information wants to be free" - a very old cypherpunk aphorism. Bitcoin's P2P network is gossip, by design - it only needs a few nodes to know about a transaction, and miners are strongly incented to be well connected to find out about txs as early as possible.

A version of bitcoin where it was easy to filter out transactions at the p2p level would be a complete failure in its most important property - censorship resistance.