Yes, you are 100% correct. In order to withdraw BAT from Rewards, you must connect the browser to one of the custodial partners that Brave supports. At this time, it is just Uphold, Gemini (if in United States), and Bitflyer (if in Japan).
Of course, this may not be a concern for much longer, as it seems you may not even be able to earn BAT anymore if you’re not in a supported region in upcoming updates.
Your question is coming at an awkward time, based on conversation you can see over at [Sweeping Changes] Brave Rewards Can Only be Earned in a Verified Profile and Is Brave fully removing the ability to earn Rewards for unverified users?
We will have more information in general on Tuesday, hopefully.