"...it isn't actually true..."
I couldn't agree more, though I think we may have subtle epistemological differences in worldview.
I think it isn't true because I'm a nihilist and I'm unconvinced that our senses, instruments, or reasoning can even ascertain the objective noumenal reality.
Essentially I think true-ness is far more elusive than it's treatment in common parlance, perhaps to the point of being completely inaccessible. Basic examples of what I mean can be found in questions of determinism in ethics, the hard problem of consciousness, and the problem of induction in science.
Here is another external link to a much shorter paper (with much less math) that deconstructs the idea of knowledge as justified true belief.
Though Gettier treats truth as ascertainable, he does demonstrate the trickiness of knowing which seems to me deeply related to issues of truth.
RE: Global Warming – Last year's apocalypse