Freshly downed live trees aren't great for firewood. The moisture content tends to make the wood difficult to light (if you can't spare lighter fluid, diesel, gasoline, candles, etc.) and it tends to produce a lot of smoke once lit. I've done enough camping that I can get wet wood burning if I have enough dry twigs, dry pine needles, birch bark, etc., but if your only experience with starting fires is pouring lighter fluid on split wood that has been dried 2+ years, you're going to have a bad time trying to get wet wood burning using only things you find in a forest after a storm.
And anything used in construction has been heavily treated to resist water damage, so I wouldn't want to be near those fumes, let alone eat something cooked from them.
It may be OK after the smoke clears. Rookies who have never used a real charcoal BBQ don't know when the coals are ready and start cooking too soon. You cook when it seems like it's too late the coals are ash but that's the time to do it.
He's talking about treated wood which is the exception. I wouldn't cook off of burning plywood or OSB but the smoke shouldn't be that toxic. Often the bottom plate of a wall will be pressure treated wood which is filled with all sorts of nasty preservatives and stuff from before 2004 was almost all treated with chromated copper arsenate. That's got a hexavalent Chromium compound (carcinogenic) along with Arsenic pentoxide (highly toxic) plus a dash of Copper because apparently the Arsenic and hexavalent Chromium weren't bad enough.
I would not cook on burning pressure treated lumber, but the vast majority of lumber in construction is not pressure treated.
Well, you're not driving off the "black bits". There's still plenty of "black bits" (unburned carbon and high-carbon compounds) in the interior. It's just that 1. you really really want to wait until the lighter fluid is burned off and 2. the whole surface hasn't started burning until the whole surface has started generating white ash. In the case of charcoal with igniter integrated in the outer layer ("match light" charcoal), I would guess you want to burn off that outer igniter layer.
As a young boy scout of 12 or so, I ate some pork that my patrol and I had cooked over charcoal before all of the lighter fluid had burned off. It tasted like lighter fluid smells. We never made that mistake again.
Pro tip from 12 year-old me: styrofoam cooler lids make great fans to speed the progression of the reaction.
Pro tip 2 from 12 year-old me: don't get the lid too close to the charcoal, or it will melt. Also, wet wool finger mittens can cook and become brittle far from a wet wood fire, because the fire gets very hot when you blow on it to keep it from going out and very cool when you go to check the temperature near your mittens.
