Based on the Symantec quote, it seems more like the NSA wants to audit the anti-virus before it gets used on government systems. So, more likely, Avast isn't asked for their source because they're not getting greenlit to be installed.
Bingo. There are certain gov organizations that you can't sell into unless you let them audit your source. It's not just the US either. Also required for certain Russian certifications (for example).