A common rhetorical flourish to indicate that you have just uttered a long, contrived, and flagrantly untrue - but not immediately disprovable - statement, and that you are pleased with yourself for having done so. Usually introduced by "At least ..." and said with a smirk and, in cheap fiction if not always in real life, setting the speaker up for a fall later.
2003.4.19@1:55 Klaproth says I ate your writeup That's my story and I'm sticking to it. We already have That's my story and I'm stickin' to it. Please repost there if you think it would be helpful. Thanks. Node Heaven will become its new residence.
In the places I've lived nobody, but nobody, would have truncated "sticking" to "stickin'", at least in writing, but the phrase has become embedded firmly in American English in this form via the Jimmy Buffett song noded here. At least, that's my story...