Every thing you said is true but you did not tell the whole truth.
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Further, if the GCWR is over 26,000 lbs, but the towed vehicle (trailer) GVWR is 10,000 lbs or less, then a CDL-B would suffice.
This is true only if the GVWR of the truck is over 26000 lbs.
If the GCWR is over 26000 lbs but the trailer is under 10000 lbs and the truck is under 26000 lbs no cdl is needed.