Consider the following scenario: The quantity of money in circulation in an economy doubles and yet there is no increase in the price level. Would this empirical evidence make an economist doubt the fact that an increase in the money supply leads to a rise in prices? Certainly not; the economist would just point out that in obtaining the said evidence, all else has not been held equal. Thus, money demand might have risen along with this increase in money supply, or the quantity of goods produced might have risen as well. Taking all the effects together, one can explain the stable price level despite the rise in the money supply.
The case of empirical evidence regarding the minimum wage not reducing employment is similar in nature.