Well there is a balance. For certain things it is natural, that you are the one giving them the information. For other things that are much smaller and much more a out generally being aware how others departments deal with certain tasks it can be enough to pick one "ambassador" that maybe does small projects with them or goes to a short weekly meeting or something.

It really can help an organization if departments are not siloed off. But sending everybody into every meeting is a recipe for not getting anything done.