You don't need any laundry service to have deniability.
I can pay you from an account I've never used before to pay anyone else and there is no way for you to find out who I am.
In the general case, even if you do things shoddily, it would still take a massive operation so you can short-list me among the possible sources of the payment.
Lately BTC's pseudonimity is being downplayed for social engineering reasons (some of the visible faces in the BTC community have decided so). Supposedly being very anonymous is very hard work now, something for experts. But in reality it's the other way around, making yourself easy to track requires very specific usage patterns. By default almost nobody gets tracked unless they want to.