I taught a couple of the GRE prep courses in college and I disagree (though not for the reasons the prep companies will likely say). The prep courses make you practice, which allows you to solve the problems more quickly and this makes a huge difference. These are timed tests.
I don't remember the SAT well (it's been forever since I took it, but I did do extremely well which helped moderate my poor high school GPA), but the GRE was based very heavily around high-school level skills that needed to be performed quickly to score well. If you hadn't solved some of these problems in years, you'd get them correct but waste time remembering the best strategy for solving them. (Trig, for instance, isn't hard but I never use it and I'm in a math-based field. It took a little while to remember how to quickly solve the problems.)
There's no need to take the prep courses to do well (I didn't), but practice pays off big and the courses encourage you to practice.