Certainly possible, but what I generally see is:
"the unemployment rate is not what [democratic administration] says it is because they redefined the metric to not include those that have given up trying to find work...the labor participation rate has dropped several percent since the beginning of [democratic administration], and the unemployment rate has also dropped several percent in that time, and these cannot both be the case."
Often the sound bytes we're shown only show the "I don't believe it" part, but if you dig a bit, at least I, generally find more context and clarification in other statements from the individual (often in an expanded version of the same quote in the sound byte), showing that the above quote is roughly the thought process of most challenging the unemployment rate statistic.
What the sides are really arguing about, as is the case with most "statistics" used in politics, is what the definition of "unemployed" should be.
Re people dismissing clear facts, again, this is just human nature. The brain finds a way to twist reality around facts that challenge foundational beliefs. The more foundational the belief, meaning the more structure built on top of it and the more decisions you have made based on the belief, the harder your brain will work to twist reality to allow you to dismiss this inconvenient fact. All humans do this, and both political wings in this country do it equally. Somewhat meta, but believing that only the "other side" is victim to this behavior is yet another example of the behavior (and we all do it).