I have one of the Harbor Freight woodworking benches that I use, and I just have it pushed up against the wall so there is no wiggle room. It is pretty solid that way. The only time the bench would want to sway much is when pushing against the handle to seat a primer, and all that force goes against the wall. I was originally going to screw it to the wall, but have seen no reason to do so.
As long as it works and you don't feel an "WIGGLE", then that is what you need. My comment was based on moving directly from a SS press into a progressive. The Dillon Tech, who is an experienced shooter and reloader, said that his bench was pretty heavy and well constructed and he has several hundred pounds of bullets and such on the lower shelf.
He MAY have been using it in a carpeted room with baseboard molding. His advice to me was that if I were in a normal house and on carpet to put a backing board (1 X 6 ) on the back of the bench. That would shim or space it out enough from the wall to compensate for the baseboard molding. I also know that in my house, the carpet tack strips cause a multitude of problems when you have a base cabinet and a book shelf unit on the top. I have to shim maybe 1/4" under the front of the base cabinets to get the bookcases parallel to the wall.
SO, my comment and your situation might not be the same. My plans, if I go inside a bedroom, were to build a work bench like the NRMA one OR purchase one from Lowes or Harbor or find a substantial base cabinet or sideboard. I would put a 1/4" thick shim around the bottom.....less about 1.5" from the rear if I had a solid base unit.....otherwise, the front legs would be 1/4" longer or have a piece of paneling tacked on. This would elevatedit to compensate for the tack strip. Carpet "sag" or crush down is probably not a factor....but if I were attaching it to the wall, then I would have two adult males sit on the bench and THEN attach so that the carpet was "pre compressed".
I would put a back plate on whatever unit I had using a 1 X 6 board or so. That compensates for the baseboard molding. THEN put in TWO 3" deck screws in one stud and do the same for an adjoining one. That is rigid. I guess my days of Manufacturing Engineering where we would have stationary machines weighing in the TONS....that would, due to harmonic vibration, start to walk around influenced me. These were basically "Bullet Making" machines....that were converted to make screws. Same process.
If you are in a room where there is no baseboard molding and the floor is tile, plywood, hardwood, etc....and can push your Harbor Freight bench against a solid wall or studs, then you probably are OK....but each installation has to be given some thought....and that is what the Dillon folks said.
One size don't fit all... And if you are in a carpeted room with baseboard molding and have it pushed against the wall and there is no "wiggle" or movement on the down or up stroke....then that works for you....and is a good solution for you.