TLDR; Binance can seize funds of users using the Binance DEX
First, it says Binance do not have access to your funds:
> “YOUR WALLET IS NOT ACCESSIBLE BY BINANCE, AND BINANCE WILL NOT KEEP YOUR KEYSTORE FILES, PASSWORDS, MNEMONIC PHRASES AND/OR PRIVATE KEYS.”
But then if you read further in their terms of usage, following text raises suspicion:
“Any use as described in this paragraph shall constitute a “Prohibited Use”. If Binance determines that you have engaged in any Prohibited Use via the Site, Binance may address such Prohibited Use through an appropriate sanction, in its sole and absolute discretion. Such sanction may include, but is not limited to, making a report to law enforcement or other authorities; proposal to Binance Chain governance (Validators and Community) for confiscation of any Digital Tokens obtained in any Prohibited Use; and, terminating your access to any Services through the Site. In addition, Binance makes no representation or warranty as to what actions Binance Chain governance (Validators and Community) may take, at its sole and absolute discretion, including to seize and hand over your property to law enforcement or other authorities where circumstances warrant.”
So if you want to be in control of your funds, stay away from it and use Nash.