Is Networking Ever Not A Good Idea?

I like building networks. Networking is usually my first impulse. Give me a job to do, and I will immediately start looking for others who are doing the same job and try to build a network with them. I’m extroverted and generally feel less smart than my peers, so a network connects me with people and knowledge at the same time. 

I’m not talking about networking for advancement or self promotion. I mean networking for collaborative problem solving, ongoing learning and experimentation, and mutual support. I mean networking as a team of youth ministers from various churches inventing things to do together that none of them were doing very well on their own. 

Not everyone is looking to network, though, because networking makes you vulnerable. Maybe the network is smarter than you. Maybe it wants to steal your ideas. It wants your time and attention, and those only go so far. 
So my question is whether a network is ever not useful.Is it ever harmful? Like any tool, a network is good at some things and bad at others. Is the impulse for networking ever counterproductive?