All else being the same, that's true. But the point is, all things are not necessarily the same. The same corporations that find labor more expensive will also find more demand for their goods because more people are earning a decent wage.
That is true at some level, but not at the minimum wage level. The minimum wage will always be too low for someone with minimum skills to earn it and own their own home, or a new car, or put away meaningful retirement savings. More than 80 percent of people who earn the minimum wage are teenagers, who live at home and are either using the money earned to have fun, or are putting it away for more advanced schooling. McDonald's isn't going to see a huge increase in sales if you raise minimum wage from $6.75 to $8.75 -- but what will happen is that McDonald's may go from working 10 people on a shift to working eight.
The minimum wage also propagates up the wage earning chain -- and what this means is more expensive goods. If McDonald's has to may a minimum wage of $8.75, then somone who was formerly paying that rate has to raise it, or suffer from having workers with only minimum wage skills. The only way the business can then maintain its profit is to make more money, and typically this is done by raising prices.
Bottom line, minimum wage increases mean there will be fewer jobs, and more expensive goods -- this is known as "inflation," as it ultimately means the same dollars buy less than they did yesterday. It's not the only way inflation can be caused, of course, but it is a contributing factor.
This is inevitably what happens when governments interfere with the law of supply and demand. It would be interesting to see what the real minimum wage would be, absent government price controls.