I'll admit, absolutely nothing is coming to mind for me about the square burn area. I've never lived anywhere one could have a bonfire or a burn pit.
Tarps have been mentioned, but if one was used, it didn't need to be plastic or polyester. I have two that are made of cloth, a canvas-like material, which is good for multiple purposes -- tying down things on your van roof, securing loads of firewood on a wheelbarrow or wagon, using as an underpad for a dog crate when traveling and needing to set the dog up outdoors for a bit, while camping, and so on. Both of mine are perfectly square, not rectangular, and they are water-resistant but not waterproof. They provide protection from ground dampness for the short term, but aren't meant to keep serious rain or flooding out.
If DM had something like that in the Yukon or the barn, it would have served perfectly. The ground was wet, which wouldn't prevent the fire from starting when you're using accelerant but would inhibit its getting going quickly. A tarp like mine would allow the fire to roar away, would not burn immediately, and might allow easier picking up of what refuse remained post-burn. After all they didn't have time for a careful clean-up.
I can't tell from the pictures what size those burn marks are, but I'm sure these canvas-type tarps come in various sizes. Mine are around 5 ft by 5 ft, IIRC. I've seen bigger ones at horse shows and the like. Never tried burning with one, LOL, but I'll bet it would leave a square scorch mark on the ground.
Just one possibility.
And, worry about the fire spreading was probably needless. The newly planted corn was just a stubble, and live plants don't turn into a scorching blaze. The ground was wet and nothing immediately flammable nearby. I always have a hose handy out in the field when I burn stuff, but I've never needed the hose. The fire contains itself because unless the area is extremely dry, once what you're burning dies down, the fire dies down too. It doesn't spread to live grass and plants in the area.
And this may explain the likelihood that neighbours or passers-by saw the fire but didn't report it (perhaps someone did, but not likely a local resident: the FD does NOT want non-emergency calls in the middle of the night. They are understaffed and need to keep their engines and crew for REAL blazes like the barn fire in Puslinch a month or so ago that killed so many horses., or a family home). If you see people attending the fire, even more reason to think the people merely don't have a burn permit(would explain burning at night) or might be contravening a bylaw, but there's rarely a reason to suspect criminal activity. Police, same story. I ran out to assist with hit and run in front of my house at 2:00 a.m.; called 911 immediately and the volunteer fire department was on the scene quite quickly, but the OPP took 40 minutes. While the officer was measuring the skid marks, I asked how come it took them so long to respond. He said they had 3 cars on that shift to cover something like 600 square km of rural area.
There are LOTS of odd things going on on a regular basis, including gunfire, little of which is criminal. Unless one is very sure something is an emergency or a crime in progress, calling emergency responders may make them unavailable for a real crisis.