If the NSA were to require them to install a secret backdoor then the NSA would be compromising the security of all of their government customers because they don't sell two different versions of their software, it is the same for all customers.
Unless the product has been certified for use with classified information, that's not much of an assurance. The government has its own internally-developed tools -- which presumably it has confidence in (SIPRNet, etc.) -- for protecting information that it deems sensitive. The NSA might well decide that subverting a commercial tool is worth the risk of compromising something that's used by the government, but only in relatively trivial ways.
I don't know enough to impugn Zimmerman et al, but I don't think "it's used by the government!" is necessarily a great seal of approval, unless it's a formal certification (e.g. NSA Type 1 listing) saying that it can be used to protect classified information. And I'm not aware of any COTS software products that are on the Type 1 list; the NSA only approves particular hardware implementations (at least that I've seen, though I'm happy to be corrected although I'd be surprised).