It's not about the 'network', it's about the wireless, and they really even ignored that in the 3 page explanation as to how it could have worked. Here's the thing:
If I'm running a wireless network in my house (not even to the internet, just computers networked wirelessly to each other), a skilled enough hacker sitting in my driveway can get in. passwords, encryption, firewalls, with enough skills and time, they get through. If instead, I've got those same 4 comptuers hard-wired to each other (and still no internet access), and there's no wireless component, that guy is shit out of luck.
It's the ACCESS that is the key, not that they are talking to each other. If it's wired and shielded, no one else gets in. If the Cylons can hack THAT, they could have hacked every single system individually in a much shorter time (because Gaeda installed the extra firewalls himself just for this, he said), and accomplished the same goal.
ANd it's NOT a pointless goal for the Cylons. Fire Control was one of the systems they were able to get into when it was networked. If they can get into that system, they prevent Galactica from firing their weapons. KInd of an advantage, don't you think? And if it only cost a couple raiders to try, they'd have done that EVERY time.
Whole thing was just bad writing, and then the writer coming up with bad justifications for the bad writing, making it worse...