Which would involve taking the system down to conduct the snapshot. What gets put back in place will depend on the severity of the breach, perceived threat, sensitivity of data, etc. They had no way of knowing exactly how sophisticated the attack was until the cops finished their investigation - is this some script kiddie or the Chinese military? I'm not going to worry about a foreign intelligence service if I'm serving up web pages for an eCommerce site, but I would if I were working for NASA. Just because you patch the vulnerability in question doesn't mean you've denied the attacker access to your network...

If they suspected additional backdoors have been added during the breach, the affected systems would need to rebuilt entirely, patched, then have data selectively restored from backup (you don't want to reintroduce to the system any malware that was saved to a backup). What other systems were accessible from the one that was hacked? Are there rootkits sending beacons home on any of them? Is there reason to preemptively take them down and rebuild them? What if one of the affected systems is a mail server/file server/etc.?

No, I don't blame NASA for overreacting. The kid pulled back technical details for a space station. The Russian government would have done the same (and may even have already been in there). NASA took steps that they thought were sensible, and they ate the costs. The kid ended up getting 6 months of house arrest and 2 years probation.