Ok you're right, maybe I have two points: I think this distraction is driven by ideology and partly maintained by (or taking advantage of) pedantry. It is far too tempting for logically-minded pedants to say "but you can clearly see what the numbers show", which is true, but is not a useful point except as further fuel for the distraction.
The real problem we're going to have is people struggling to find jobs as demand ramps back up slowly in fits and starts. This whole conversation is an attempt to portray those struggling people as the problem. It is indirection, like in a magic trick. And the pedantic "well actually"s are falling for the trap.
It's a real bummer because it's definitely going to work, which is going to cause us to underinvest in unemployment insurance over time, which is going to make this even more painful than it was already going to be. It would just be nice if people could see that they're being played.