The reason you get lateral forces against the rack is because either (a) you don't hit both J-hooks simultaneously when setting the bar down or (b) for a bench press, if you follow Rip's instructions, and slam the bar into the uprights (okay slam isn't the word used in the blue book but I don't remember the exact quote), you aren't going to hit both uprights at the same time.
The asymmetry will create some degree of lateral forces. The RML-390F weights three hundred pounds so you have a lot of inertia to work with there and the triangular reinforcements clearly add some amount of stability. On the flip side, when you rack a bench a bench, the bar is going to have a mechanical advantage such that the front of the rack will lose contact with the floor just long enough to move a small distance.
Again I'm paranoid about this stuff (but I've also never lost any teeth or gotten killed benching) so if you don't want to use a cross-member, after setting up the rack, measure to be sure that it's square. Then mark the floor around the base with chalk so that you can see if it moves.
Or you could buy the SS rack.