Can I install it so the rings or brush face towards the rear of the rack?

Yes, it is physically possible, but it is an alternative orientation rather than the arrangement the product is principally intended for.

There can be perfectly sensible racks in which facing the rings or brush towards the rear produces the better route.

I would only do it where the cabling gives you a reason, though. Reversing the panel and then creating a convoluted path merely to reach it would solve a problem of our own invention.