So what we learn is that funds shouldn't be deposited to a centralised exchange directly from any third party. You should bring the funds into your non-custodial wallet first. Then you should use CEX to buy crypto coins and move them again to a non-custodial wallet. In the meantime, if the exchange is about the source of funds, you can show them with video proof, etc.
Even this method has long been out of favor for Mixer transfers. This happened to me personally when I was a Binance user before finally leaving it. I withdrew Bitcoin directly from Mixer to one of my own addresses before depositing it to my Binance account. My deposit was frozen, and I had to wait two days before I could use it. Support didn't provide any specific explanation, and they simply said it was a common suspicion that needed to be verified. This happened again when one of my clients sent me a Mixer transfer to a new private address. I then deposited to Binance, and the same thing happened. This ultimately forced me to leave Binance for good.