Not even close to the truth.
You aren't going to have a lot of fun on something like Mount Hamilton road or Nacimiento Ferguson Road west of Fort Hunter Liggett with a rear tire wider than a 180. That's why little skinny tired bikes like R-1100GS's and SV-650's rule the tight second gear roads and things like Ducati's and R-1's get eaten alive on these roads.
I'v seen enough egos on expensive big bore sport bikes fall to good riders on a bike with laughably narrow tires. While a Ducati is magic banked over skimming fairing panels at triple digit cornering speeds, slow them down to second gear and throw a bunch of quick transitions at them and they fall flat on their face. Different tools for different jobs.
I can tell you that going with a narrower rear tire on my Street Rod did wonders for the steering, particularly on tight roads. Now it is dead neutral where before you had to keep a bit of pressure on the bar to keep it turning.
You say I don't know anything but how much experience do you have riding tight mountain roads and on what kinds of bikes? I'm not exactly inexperienced, I've carved canyon roads on three continents.