Looks like they used SQL injection to get passwords and then used those passwords to access the servers.

Yeah, and that's from the application layer down to the DB layer. I wonder how they were able to pass through the other layers of the stack. I heck of a work, no wonder they'd spent "months" on it.

...crazy.

The article says that they used the injection to get hashed login credentials. Did they then use a rainbow table to reverse the hashing?

There are a wide myriad of ways that plaintext can be derived from password hashes. Rainbow tables are an option if they're not salted; otherwise the attackers likely had access to fairly significant computing power (considering the amount of money they were raking in) to perform typical dictionary + bruteforce attacks on them.