Is this from Autogeek? In their Speed Master line?
If so, I don't remember ever using this exact brush but I have used the brush that looks like this that uses Boar's Hair and claims not to scratch paint. You're also supposed to soak the Boar's Hair brushes for 30 minutes in warm water before use.
I remember testing out the boar's hair version to wash my own truck and it scratched the hell out of it.
My guess is, brushes may be safe on cars with really HARD paint, but anything with medium to soft paint - you're going to see scratches. The below picture is all that's left in my article when I used the brush to wash my truck. Since the geek upgraded their forum, a lot of pictures are now missing.
Then I re-polished to remove the scratches.
I do remember using the same brush to wash a Mercedes-Benz we had at the time that had the PPG Ceramiclear and I didn't see any scratching on the MB paint.
Below is the paint that came on the above white Mercedes-Benz.
Me? I'm a fan of the chenille microfiber wash mitts.
Besides how well or horrible any type of wash mitt works; BESIDES the actual washing process, the other thing you need to consider is how easily or how difficult it is for your wash mitt of choice to become CONTAMINATED and then how easy or difficult it is to WASH OUT the contaminants so that you don't scratch your car every time you wash it.
The mitt I show not only is safe to use when washing a car, but it CLEANS EASILY when washed in a top-loading washing machine with an agitator that goes nuts.
And I know a lot of people don't have washing machines that actually clean things, but that's their issue. Here's a recent video on how I would wash a car with a pristine finish without the use of a foam gun or foam cannon.
The 1963 Avanti in the above video has been accepted to be entered into the Amelia Island Concours.
Mike