From my perspective, the last sentence is just incorrect. There is a lot of work by reputable economists that finds adverse employment effects of a higher minimum wage. In a poll of top economists, as many say they believe that the adverse employment effect is noticeable as those that say the opposite.
Now, we all know the arguments that have been used against a higher minimum wage. Some say it actually hurts low-wage workers -- businesses will be less likely to hire them. But there’s no solid evidence that a higher minimum wage costs jobs.
The president could have said there is no completely decisive evidence. Or, more accurately, he could have said there is mixed evidence. But saying there is no solid evidence is misleading.