To me, simply saying "False." with a link is not any colder than saying "That is false." or "that is untrue, see this ___", etc..

I admit, I agree that "Lie." was a little on the cold side. I find that when people blurt out something so obviously and verifiably false that they are either being lazy or facetious which also does not "lead to a constructive conversation". Perhaps if I had the ability to downvote it I would have done that and moved on. Not an excuse, just an explanation.