If his was really true for banks there would be a large number of bankers in jail. This number being close to zero, I guess the courts are very lax at charging bankers for crimes.
A bank will drop you if they even think you might be doing something (demonstrably on paper) illegal. When opening an account, some of the very first questions a bank asks you are "where did you get this money" and "what do you do for work" - proactively making you responsible for committing to some type of story. All of the illegality you're trying to reference is happening under a backdrop of reams of paperwork that make it look like above board activity to compliance departments. Without that paperwork when shit does hit the fan, people working at the bank do tend to go to jail. But with that paperwork it's "nobody's fault" unless they manage to find a few bank employees to pin it on.
Needless to say, this type of prior restraint regime being applied to free-form communication would be an abject catastrophe.
Any source for that? Media loves to blame banks for everything, but when you go into the details it always seems pretty marginal (e.g. the HSBC Mexico stuff).