Abstract argument here is useless.

Well, as point out here your abstract argument doesn't hold up to looking at the details.

comparing minimum wage increases with teenage employment over time and such. Which has to be active deception / malice - increasing educational attainment over time is the actual cause of variation in that variable,

I assume you mean that the reason for the drop in teenage employment is that they're spending more time in school and/or studying. This is not at all obvious, after all most teenagers have been attending high school for >50 years. Traditionally they'd take part time jobs in addition to attending school.

Going to go dig through OECD databases to find median, minimum and average pay, and graph against labor force participation.

The claim was specifically about minimum wage. This is quantitatively different from median and average pay. Minimum wage is determined by law, whereas median and average pay are determined intrinsically by the economy.

Also how are you planning to compare wages in different countries?

I expect median to have the largest effect.

I also expect median wage to be positively correlated with employment and suspect you have the causation reversed there. The better the general economy is doing, the more demand for labor there will be, the higher the median wage will get bidden up.