Doing the local backup and copy the bak file to nework location is good idea but when you don't have the space, you have to use network backup....

If there is any issue in network backup job will fail. When the backup is running SQL sends the packets waits for aknowledgement from the host, incase on no aknowledgement backup job will report you as failure even it is completed 100%...

I am doing nework backups since 7.0 without any major problems...

If some ask the water on the other side of the room you can ask them to use the tap if there is any and if you have the switch for that tap you need on it...

I beleive network backup is like running the pipe for water...