The revelation is that the official unemployment rate is so skewed it is meaningless, even misleading since high unemployment is a serious social issue thus should be a high priority political concern.

There is no revelation. The authors are intentionally misleading you by comparing 2 different metrics to pretend their formula is meaningfully different than what BLS provides.

"Headline" unemployment rate is U-3 unemployment. If they compared "TRU" to it's analogous match U-6 the graph would be less striking as it's a 1:1 match.