I wouldn't have needed to eliminate the threat the first time if there wasn't proof. But yes, he tried to use to knowledge against me and discovered that Hux already knew. Or so I was told. I don't know what he hoped to achieve by sharing the information - to undermine my position and lift his own, I imagine. But the fact that attained the information from an incredibly biased source who no doubt spun the tale towards certain personal advantages makes him dangerous.
You have the first half of my confession. If I'm to give the second half of it to anyone, it will be you as well, not him. I won't give him any more ammunition to fire at me with.