So bank should be held liable if they:
- do not collect evidence
- do not act on evidence
- if they act without evidence
The bank should face appropriate penalties for making misjudgments in both directions. For example, you should have a right to sue bank for refusing to provide a service. The court could judge whether bank had sufficient grounds to refuse to conduct the business with you.
The bank should also provide the evidence to law enforcement to trigger investigation into alleged illegal misconduct. If the judicial systems clears you, then again, you should be able to compel bank to provide the basic financial services.
There is regulation like that for individuals in EU. Banks are obliged by the law to provide basic financial services (bank account and identification services if I recall correctly) to EU residents as part of the European Single Market.