Yes, they can. In addition to the other answers detailing the reasons why that makes sense from the companies point of view, I would like to add why this makes sense from the employees point of view:
You need to make sure your company knows you are working that day. Although probably this is different from country to country, there are insurances that cover most of what you do. Get into a car accident? Insurance. Got hurt at home? Different insurance. Got hurt at work? Yet a different insurance again.
Lets say you get into your car on your way to work and you have an accident. Where I live, this is covered by the "got hurt at work" insurance, because it happened on your way to work. If however, the insurance company can get it's hands on a testimonial from your manager, stating (quite correctly, because you never let him know) that you were not supposed to work that day, guess who is more than happy to not pay your costs.
So having your manager sign off the change in plans is required for the safety of both parties, the company and the employee.