My theory is that J'onn actually knows about Bale-Fire: The white martians made a number of attempts to rule earth during the historical period when Karfang wasn't the last of her kind, and if you assume that bale-fire is something all or most dragons can do, then it's pretty obvious that White Martians were fucking terrified of the things. I mean, you're a White Martian. You've got shape-shifting and psychic powers and use those abilities to deceive and subjugate sentients who are far less powerful than you, and fire is your Only Weakness. Then there's these dragons. They're tough to kill, live forever, have a hostile attitude, and can breathe fire that burns lies. That's the kind of news that makes it back home where your hippie neighbours would hear about it.
Alternately, as soon as he could do something with himself, he felt justified in making a thorough mind-read and picked up on the whole "fate worse than death, followed by death" that he just got saved from.
As a corollary, the White Martians are almost certainly responsible, though probably indirectly, for the near-extinction of dragons.