I don't understand something here. When I use an exchange, such as Coinbase, they do all the work. Or at least get it started. When I use a wallet, such as Trezor, the request is submitted to the Bitcoin network and some number of the Bitcoin nodes validate the transaction. In the response you wrote, I get the hint that I might need to do something more to validate the transaction. Please explain a bit more.
What he meant was that those wallet or exchange that you use to broadcast your transactions rely on third party nodes to validate your transactions and this will hinder your privacy because your IP address can get exposed, there by exposing your physical location. With your personal node you wouldn’t also rely on block explorers to verify the status of your transaction.