It’s a true claim actually Atomic swap to Monero provides an effective solution for Doxic change outputs. But if you are swapping into Monero, you would be well advised to not swap back immediately. Best to wait a little bit before doing so to avoid the guess first heuristic.

You would also want to avoid sending the same amount back as this will allow simple amount correlation. Monero's opaque blockchain has privacy advantages but whirlpool does a good job breaking deterministic links and providing forward looking privacy. You would need to determine your level of privacy requirement and transact accordingly. If you want to stay in BTC the whirlpool is best solution and swapping doxic change to xmr is effective for that use case. Also liquidity is def an advantage in BTC's favour.