yes the overall transaction is safe but the individual node sending that transaction/block is recorded with the IP logged. Mass collection with a large spy network would easily enable a semi reliable initiator logging system that could be used later for any purpose. You could connect to a public node to hide and not send from personal node but then again the public node itself could be a spy node too. Its all about collecting general metadata for use with other data to be cross examined when the time is needed.

Best solution when connecting to public nodes would be through Tor. Even if the public node is a spy node somehow with tor enabled, they would still be able to see requested blocks but would not be able to pinpoint who is requesting. It still adds a good layer and is recommended by most, but it is not perfect because Tor is also somewhat under a timing attack.