If in a questionable position, you're 100% right. Take the scale and let them wave you on or bypass. Only takes a couple minutes as long as everything's legit.
From your quoted article, "If you operate a vehicle over 10,001 pounds Gross Vehicle Weitght Rating (GVWR) or Gross Combination Weight Rating (GWCR) in a COMMERCIAL BUSINESS, then you are considered to be a motor carrier. You do not have to haul freight to be considered a motor carrier. If you are in BUSINESS then you can be considered a private carrier and subject to the FMCSRs."
Which is not the same as a private - not for hire - non-commercial vehicle. As long as it's for personal use with no monies exchanged. Now, let's say you've got a 1 ton p/u and a wedge style fifth wheel with 2 or 3 vehicles loaded. Odds are you'll get stopped for blowing off a weigh / safety station. If all of the towed vehicles are titled to you, no problem. No titles or registration in your name? Now you are dealing in commercial traffic. You would need a CDL, medical card, triangles, fire ext., log book, U.S. DOT numbers (if out of home state) plus fuel and use stickers.