Sorry, but the big dopey head on yer one. The whole story sounds rubbish. From the dog getting the scratch on its nose, to yer man throwing sticks at it. First reaction would be to keep your kid safe, in such a situation. Also, if the natural reaction of these "big cats" is to just stand there and attack whatever comes it's way, instead of taking off, we'd have tons of footage/evidence.
I mean, their either elusive, or their not.