The key to your question actually lies in the understanding of what "System" is. Here are a few things to remember about "System"
1) No local profile.
2) No access to network
3) Full admin rights to local
Now, put those three together with various situations and you'll get the answer to your question. For instance, the system account may not have access to network resources, but if you supply credentials, then you can get out. Thus, the need to supply credentials. System may not have a local profile, but if your software only installs to HKLM and not HKCU, then you're OK, right? HKCU is the local profile (well, part of it). System can install software that goes to all users, but not to a specific user.
That also answers why System is able to get to the network. It doesn't, really. The other account you supplied opens that door for System, and then System simply executes the stuff locally. In a way.... OK - that's over-simplified.
Anyway, the problem is making the assumption that because System works in one scenario it'll work in all of them. Truth is, MOST software will work with System rights just fine. But not all. The key is not ALL. So long as you remember that, then you're good to go.
PS> WinPE ONLY has a System Account. Thus, if you try to execute something in the context of a specific user... guess what? It wont work! If you have something you need to run in WinPE that requires you have a local profile - too bad. Now we know why. :D
GL moving forward. Glad to hear all is going well.