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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.
It's definitely best to rely on the written terms and policies, especially the AML and privacy policies. What the customer support tells you can sometimes be unreliable, even if they're well-intentioned. I also always take screenshots of important messages when I chat with support of different services, just in case they decide to go back on their words.
It's worth trying to find out what third-party service they're using for that analysis, although I doubt they'll disclose that information.