If the manufacturer said don't use a cord then don't use a cord plain and simple. This also means that a Nationally Recognized Testing Laboratory has tested the piece of equipment without the use of a cord therefore the manufacturer of the equipment must include the verbiage to not use a cord in their instructions.
So, plugging directly into a receptacle at the end of a daisy chain of 7 or 8 (or more) receptacles, wired in series using 14 ga. in the push-in holes in the back, is OK. Using a new 12 ga. 9 ft. extension cord, plugged into the first receptacle on a circuit wired with 12 ga., using screw terminals, is not OK because it introduces an extra spring tension connection. According to the manufacturer's installation & use instructions.
Personally, rather than attempt the calculations, I'd plug in my Kill-a-watt and monitor the voltage during a use cycle. And feel the temp of the connections at the end of use.
I'm all for safety and durability measures, based on reality and actual conditions. I retrofitted GFI and AFI, notwithstanding my homes were grandfathered. I've gone through and redone all the receptacles that the builder pushed the wires into (code acceptable). I use 20 amp spec grade receptacles for things like the laundry, refrig, freezer, microwave, for the safety & durability margin they give.
(I also toss tires at 4/32 and change oil at 3 mo/3 k miles. I change tranny fluid at 15k and fuel filters at 60k, even though the manufacturer doesn't specify any interval.)
I'm curious about one technical point: Does the quoted statement mean that any listed equipment which does not contain the "no extension cords" warning
has been tested with extension cords?