False. This may have been the case back in the Silk Road days but Bitcoin can definitely be traced now. This is why many deep web markets have switched over to Monero.
If you ONLY deal from bitcoin to bitcoin it is possible to remain anonymous... the problem is that most people, at some point, buy bitcoin with fiat. If the government/someone really wanted to track down a transaction, they can do so even through bitcoin mixers and whatnot.
If you want to be completely untraceable, you must procure your bitcoin in an anonymous way and never deal with a fiat/bitcoin conversion business or any other entity that is tied to your identity.
Once you have a business such as Coinbase in a transaction chain, they must respond to lawful subpoenas for customer information. If they do not, they will face serious consequences. Some bitcoin businesses also have in their terms and conditions that they can choose to voluntarily comply with a request from a law enforcement organization for information, rather than requiring a subpoena.
Best regards,
Ben