All dependent on context. In the context of a team, one can rarely solve all problems by herself. More importantly, it can cause greater disfunction when work isn't coordinated/communicated appropriately. The whole point of working in a team is to get more work done more efficiently because the work load is shared and each member focuses on her specific skill, and doesn't do everything.
Yes, context is key. My implied context was small problems that can be solved with just a little bit of programming. If the problem is big enough to require a team then a different approach is required.
