He ain't wrong. Chemical weapons weren't used against military forces in WW2, despite pretty much everyone having the capability.
One version of events is that when the BEF evacuated from Dunkirk, right near the start, amongst the various other supplies they left behind in their inauspicious (but, arguably, glorious) retreat was pretty much every chemical shell the force had (having expected something similar to WW1 happening again).
It is said that the discovery of these by the advancing Germans was interpreted as basically "if they've so casually discarded these stocks, they must have
many times more still deployable..." Germany had been somewhat more compliant than the other powers in not stockpiling their own gases (prior to the development of their more (im)famous nerve agents), and so did not feel like getting into a pissing contest with anybody they suspected to be so capable of retaliation. They even
assumed that the Allies had developed at least as potent a weapon as they recently had, imagining their lack of intelligence on that matter was just down to good secrecy on the various opposing development teams' parts...
(Adolph, having been a gas survivor in WW1, also kept the ultimate authority for their use mostly in his own hands, perhaps for that particupar personal reason.)
Meanwhile, the British defence against invasion would have involved 'mustarding' our own beaches, with urgently rebuilt stockpiles, as well as against German cities if at any point the Germans used 'their' stocks, and similar plans to (re)retaliate against cities if there had been gassings of our D-Day forces by the Germans. A precursernof M.A.D., that may never have come to pass only because all sides' imaginations actually outpaced the capabilities and intentions of the others, and yet no false positives set that particular stack of Jenga bricks to tumbling down.
Not that WW2 was Chemical-free, especially over in the Sino-Japanese theatre and in clearing out Russians from caves after a comprehensive defeat
on the ground near Sevastopol, and there were accidents (including stocks compromised by enemy action) of various kinds.
Although better historians then me may have more definite information than that which I received mostly as hearsay.