You have a misconception of the AML and KYC directives. It's the same thing, the KYC directive is a part of the AML laws.

Under the the name AML, there are:
- KYC: know your customer
- KYCC: Know Your Customer's Customer. Yes! customers of your customers
- KYT: know your transaction
- KYB: Know your business
- CDD: customers due diligence
- SAR: suspicious activity report
- PEP:  politically exposed person
- and so on...

Do you think they don't check the source of the funds? They do, as well as the banks involved in both sides (since it's also their job).
Do you think Kraken doesn't do that while it has a Money Business registration.
Why do you think they all have paragraphs about AML on their ToS,