What is the time frame for these claims? The last few years when the new minimum wages are coming in are also times of dropping unemployment. The area I live in has not been raising minimum wages any, and the local "minimum wage" has nevertheless become a de facto 11-12$/hour for zero-skill jobs just due to a tight labor market.

If you happen to time your raising of the minimum wage to when the market was tightening anyhow and the market floor was going above your minimum wage anyhow, you won't see any negative effect, but not because you can just raise minimum wage with no effect, but because the market beat you to your raises. It's useful information, but not politically useful information, in the way that people are looking for. The question we really want answered is whether we can raise the minimum wage significantly above what the market would have done anyhow.