Are there times when you shouldn't follow procedures, when you should go against the rules? Probably.
In the military, we could refuse a direct order from a senior person under certain situations. It didn't happen much (as it shouldn't or military order would fall apart) but sometimes you should just say no.
I've been on projects where stakeholders were asking for features that I had to push back on. In some cases, the requests weren't in line with the vision of the project. In some cases, the time line would be effected. Sometimes they were just bad ideas. As the project manager, I had to tactfully refuse and point out to my stakeholder why I was doing so. In most cases, a compromise could be found.
On a similar note, we should know when project procedures should be modified. A good example is templates. I have a number of colleagues that think templates are a bad idea in general. When they are used, they can be used without thought. Since every project by definition is unique, we shouldn't just fill in templates without thinking about how they apply to our projects, or if they apply at all. They may be boxing us in, preventing us from being creative in our approach to the project.
So next time you're working on your project and some process, procedure, or template doesn't seem right, maybe you should just say no.