It isn't fake. It aligns with the reality that hits you when walk outside. Everybody that wants a job has one. The labor shortage is visible to the naked eye.
And politically It would been better for Republicans if the labor participation rate was increasing. At least then they could have said "inflation is driving poor helpless retirees back to work".
Their red wave hopes are dashed because gas prices are going to fall straight through to election day, unemployment is almost nonexistent, and we are going to say it's the Inflation Reduction Act's doing. And all you will have is "your world is a mirage" argument.