I would never trust or rely too much on the words of low-level customer support personnel. They will tell you all the sweet things you want to hear or forget to mention what you don't want to hear. The only thing that matters is what is written in their terms, not to mention AML and privacy policies. If there is a separate AML policy document, your questions regarding KYC and other checks are answered.

What is surprising is that they were willing to scan and analyze your addresses and coins for "risk" and "taint." I haven't heard that before. Try to get them to say what third party they use for that analysis. I doubt they will, though.