While it makes sense that at least initially you would probably use less brain power due to the lack of some stimulus in VR, I think they're also missing another interesting fact. In humans, when we lose one sense, it tends to amplify the abilities we have left. Take a blind person for example. Some folks who are blind develop the ability to echo locate (sonar) so accurately that they can walk around blind and identify objects entirely from the sound bouncing off of them. The brain also rewires itself to handle sound processing more than visual.
Also when I was younger, I use to play on the text based social MUD VR like systems. Despite being text-based however, they used your imagination to fill in the gaps and if you got into it, it could almost be real. I compared it to reading a very good book with yourself as the main character. I know that before that point in my life, my reading and writing skills were no where near what they are now. What eventually amazed me even more was the ability to pick up on real-life traits based on the things people wrote in their VR character profiles. While I can't claim to be perfectly accurate, I was a little surprised myself when I outright guessed a few details about some folks online before I asked them about it to double-check.
I would bet that in that situation my brain activity probably would start out low but due to our intelligence (or imagination) that we have over rats, it could potentially amplify with time.