Explain road force balancing:
It is primarily a) a marketing gimmick and sometimes b) a method used to quantify exactly how shitty the rubber industry has become. It really has no impact on the customer, other than sometimes being a number cited when warrantying tires.
Anyone who talks about how it allows for optimal match-mounting of tires is full of crap. Wheels are round and do not have notable variations in density (not that the machine could measure the latter, anyway). Rotate an oval tire to any position on an unbent wheel and, surprise, your tire is still an oval.
So you're left with it just being a number. It is not the same as balance. Tires can be in balance* and still have a high road force number, which basically just indicates a significant amount of radial runout- 'road force' is the amount of force that the lopsided tire is thwacking the ground with every time it rotates. Significant lateral runout can be present with both 'perfect' balance AND a low road force number. Lateral runout, though, will usually only cause issues on the steering axle (this is where steering wheel 'shimmy' comes from). Your average felt vibration is generally a function of radial runout and/or imbalance.
*'in balance' meaning the machine says zero. I could put five pounds of of unneeded weight on a wheel/tire and get it to show zero on a balancer. It will still cause your teeth to be shaken out of your head. Even basic balance numbers are meaningless if the balancing is not done right. I.e. dynamic (not static) with one group of weights on each side of the wheel (no 'counterbalancing').
More important than all that, OP:
Your tire shop is incompetent and the dealer is lying. One of your front tires was out by about an ounce and a half. Most decent non-truck tires will take...about an ounce and a half of weight. They probably still don't have it right. Check your wheels for copious amounts of randomly-placed sticky weights. Most 'tire techs' are too retarded to pry off the old ones before putting additional ones on there.
Beyond that, their supposed 'after' road force numbers are fabricated bullshit. The one single wheel that was in balance went from 23lbs (pretty damn high) to 3lbs (unbelievably low) due to...what? What did they do? Fart magical pixie dust onto it?