This argument usually doesn't work because if you consider a different subset of the people who aren't working, you must then compare it to a different baseline. So being able to pick a different set of people to call unemployment (e.g., people not in labour force) doesn't actually let you claim the things are much better/worse, you still need to work further. In particular with respect to the labour participation rate, I think it's well known in leftish circles that it went down quite a lot in the GFC and that that represents a problem. I don't really know where you got your impression from.
In any case, I disagree that that's the argument they are usually making when questioning unemployment statistics. It could be their argument, but they'd have to actually make that argument. There usually isn't much beyond just rejecting statistics, unfortunately.
Furthermore, there is demonstrably a lot of people who think the inflation figures are downright made up (even here on HN), despite plenty of evidence to the contrary. In fact, the inflation example is even clearer, due to how little leeway there is in deciding, for example, what to call inflation.
In any case, I didn't call them "stupid" and "crazy" because they "didn't subscribe to my preferred narrative", as you put it. It definitely wouldn't be stupid or crazy to make the argument you are making. There has been plenty of discussion in economics history of which measures best represent the state of the economy. However, if someone, as many politicians do, feels comfortable enough to reject that because they don't feel it's convenient, then, sure, "stupid" and "crazy" are decent enough words to describe that particular behaviour.
After all, just because I can come up with a better argument for someone's position, doesn't mean I can substitute the argument they made with a different argument that I find more reasonable (it would be distinctly uncivil). Specifically with respect to unemployment rates, you and I may simply have been reading different things, but I believe what I said was accurate.
One further thought: the unemployment rate (not the participation rate) is part of the Federal Reserve's mandate, and it is the rate that has traditionally been used, with perfectly decent theoretical justification, so I feel quite comfortable saying that it's not some kind of left-right partisan divide.