Then surely we can open source F16 source code and publish it on Github.
In the case of web code, there's nothing's new and innovative about the software that is unknown by existing developers. There is the potential for exploits but open source can help plug up those holes by allowing the community to assist in the process.
Sure, dumping the supposed "500 million" lines of code all at once would make it hard to review but they could release one compinent at a time over several months/years and vow to release all future code.
On a side note, wouldn't reviewing and repairing govt software be an excellent teaching tool for schools? How proud would a child be to have their code fix be accepted into production?