hi csl,
it is evidence which contributes to DISPROOF of the widely-believed theory that increasing the minimum wage also increases unemployment. associating minimum wage increases with employment loss is the argument people often make - but without evidence and based only on what seems like common sense. and yet evidence for that claim cannot be seen in the available data.
when the evidence doesn't support the hypothesis, the hypothesis fails. or needs to be refined.
of course various factors are involved. much of economics is based on the phrase pari passu, all things equal. but if you can't isolate a connection between the minimum wage and unemployment rates, and even unisolated situations show no relationship, then the hypothesis about minimum wage increases increasing unemployment hasn't any useable value.
so the observations you made about various factors obscuring the hypothesis actually support my point, which was "it won't stop anyone from saying that raising the minimum wage increases unemployment." this experiment suggests the claim cannot be sustained. perhaps because other factors influence the outcome, as you say. anyone who makes it defies the lack of evidential support for the theory. but i have no doubt that people will repeat it ad nauseam.
by the way, i am not arguing that raising the minimum wage increases employment. but it doesn't seem to affect it negatively at these levels and in circumstances such as these. so the theory of the baleful influence of minimum wage increases isn't a rule with universal, if any, application.