It would really depend on where you are located.
Here in the US there is a big emphasis on Mens rea
https://en.wikipedia.org/wiki/Mens_reaSo there is the element of what is going on. Using your HSBC example they knew, but it was going to be just about impossible to prove who knew what and when.
If some shifty looking person shows up at my shop and I take in a few thousand in cash and take a cut and give it back with a 1099 tax form it's fairly obvious what I was doing.
So that is going to be a big part of it.
If you are wearing a signature for Bob's Meth and Heroin shop it's going to be a much more difficult thing to talk your way out of then say [looks down at signature] ChipMixer which is a legit service for people who just don't want to be tracked.
-Dave