LocalSystem vs NetworkService

Hello everyone!

I'd like to clarify a theoretical question concerning LocalSystem account.
There are plenty of articles and other documentation telling us that services running under the context of the LocalSystem (and LocalService too) account can not have access to other computers while those running under the context of the NetworkService can.

Having read this article (http://msdn.microsoft.com/en-us/library/windows/desktop/ms684190(v=vs.85).aspx) carefully I could not find the difference between LocalSystem and NetworkService accounts regarding network access:

LocalSystem:
"It has extensive privileges on the local computer, and acts as the computer on the network. "

and "The service presents the computer's credentials to remote servers. "

NetworkSystem:

It has minimum privileges on the local computer and acts as the computer on the network.

" A service that runs in the context of the NetworkService account presents the computer's credentials to remote servers. "

So why the LocalSystem account should not have network access when it can "presents the computer's credentials to remote servers" in exactly the same way as the NetWorkSystem do?

Thank you in advance,
Michael