You know what's weird about the word uncomfortable? Literally, it means that you're in a state of discomfort so bad that you cannot be comforted. But of course, an uncomfortable person can be comforted, sometimes very easily. If you're uncomfortable in bed, you can fluff a pillow. If your headache is making you uncomfortable, you can take some Advil. If your neighbor's racist jokes make you uncomfortable, you can deck him.
That means that if you're comfortable, literally speaking, you could be comforted. But comfortable, the way we use it, means you're already comforted.
Also, incontrovertible facts is redundant. If something's a fact it cannot, by definition, be controverted. An assertion can be controverted, a theory extrapolated from facts can be controverted, even a conclusion can be controverted, but a fact is a fact is a fact.
Also, unflappable is an odd word, as the title of this blog demonstrates. Flappable is almost never used. Plus flap, in slang, probably refers to the thing a bird does when it gets all flustered - you can't flap a bird, the bird is the flapper. Likewise, you can't flap a person who's flappable, they have to flap themselves.
Go flap yourselves.
* Quote from Scrubs