Cross-functional teams and dependencies

How cross-functional is a team that's often depending on someone outside of the team?

One of the important traits of Agile teams is that they are cross-functional. The team should be able to create an increment of value without external help. But I often talk to people complaining that their dependencies are killing their effectiveness. Agile teams could have the occasional dependency on people outside of the team. But it’s often a struc…