the hiccup there, as you identified, is when files exist on the network, and not the local disk.
The system account is one of those special accounts that never logs into the domain, so it doesn't get access to any network shares.
If the instance ever needs anything except local disk access, I usually create a new user like SQLAdminMachineName in ActiveDirectory, and give it the network shares it needs access to, and use that as the startup acocunt for the service instead of the system account.
Lowell