A minimum-load or short-load fee holds up only if your own terms name it, at the rate they name, on a load that was actually under the minimum. We read the fee against the quantity on the signed ticket behind it, and we flag the same charge riding one load twice.
One corpus job bills a flat short load charge of $150.00 on its 3.00 and 4.00 yard tickets and nothing at all on either 5.00 yard ticket, same purchase order, same week. Another supplier charges a short load on one job and leaves a smaller one uncharged on another. The threshold and the rate live in your terms, not in a default we assume.