Early in my genealogy quest, I found several people researching parts of my family tree. I eagerly copied down their information only to realize later that some of their research was flawed. That is when the important to doing your own research hit me. Had I not came across information that showed me the previous researcher was wrong, I would have wasted a lot of time tracing the wrong family line.
As you build your own family tree, you will probably come across people researching the same ancestor. If they have sources to back up their links, that's great. If, however, they don't, you really need to explore to make sure that the links are accurate. Otherwise, you risk wasting time and effort on a fruitless task.