Where did you see that? I'm using Brave right now and I don't see them asking for KYC anywhere. Actually, I just opened the rewards tab and they gave me free 4 BAT.

edit: all I could find is KYC for publishers[1] (owners of websites that want to receive BATs)

[1] https://community.brave.com/t/uphold-kyc-know-your-customer-verification-is-now-required-in-order-to-receive-bat-publisher-payouts/42035