That's the point. Absent any competition (which there won't be, because everyone is subject to the same minimum wage), the cost is fully passed on to the customers (ie. "everyone else"). Therefore your conclusion is incorrect.
In the short term or long term? I skimmed the study and it looks like they only looked at two years? In the short term I can see it happening due to psychological effects like price stickiness, but I'm skeptical that in the long term the trend would hold. As evidence to the contrary:
>Ashenfelter says the evidence from increased food prices suggests that basically all of the "increase of labor costs gets passed right on to the customers."