> I ask because lots of things like welfare payments and estimates of poverty level involve comparisons with the MW

Can you give an example of such a welfare program? I'm not aware of any that use the minimum wage as a baseline. Most use the federal poverty level, which is pegged to the cost of food (and is updated yearly for inflation).

> It's sometimes advantageous for a politician to say...

I don't really care what politicians say; I'd rather have policy be evidence-based rather than reaction-based