While I obviously welcome people being paid a reasonable salary for their work (and there’s nothing unreasonable with a salary of $15 per hour), I think you’re jumping the gun here somewhat — you’re leaping to conclusions on the basis of single study of a single economy. Even the authors of the Berkeley study you reference acknowledge that “any assessment of the impact of Seattle’s minimum wage policy is complicated by” the “complex array of minimum wage rates”. Furthermore, similar reports are planned for Chicago, Oakland, San Francisco, San Jose and New York City, among others, when data of sufficient quality becomes available — in other words, the Seattle study can be considered a somewhat preliminary investigation.
I think it’s also worth considering that Seattle’s historically low unemployment rate (which may be indicative of “under-employment”) may be playing a role in driving salaries upwards. Although admittedly, there is potentially something of a chicken-and-egg scenario here — are the higher minimum wages driving economic growth which is in turn driving down unemployment, or is the economic growth driving demand for labour and therefore driving up salaries?
Finally, as a scientist, I’m afraid I must point out the flaw in your vitamin C-cancer analogy:
If they’re studying the effects of Vitamin C in rats, they’ll broaden the study to try to confirm their understanding of the world. When they can’t find a direct tie between Vitamin C and cancer, they’ll find anecdotal evidence and wrap the entire study around itself to prove their beliefs.
Any scientific paper based on “anecdotal evidence” and “beliefs” is highly unlikely to be published and even it did somehow make it through the peer review process, the shoddy methodology would see it dismissed out of hand by others in the field. Science seeks to test a null hypothesis. In the above case, that null hypothesis would be “vitamin C does not cause cancer”, because as you rightly point out, one cannot prove a negative.