You don't know why our war department would not want to pay foreign nationals for code that they intend to use in a battle situation? Is it honestly that hard to figure out why that restriction might be in place?

DARPA has a ton of research done by foreign nationals. (I have worked in labs which have foreign nationals who get paid to write code for DARPA projects).

They will audit the code, no matter the nationality of its author. There are plenty of US residents who would sabotage the code if they could.

Would they rather want them to give the code to, say, the Syrian government?

It is not like they can't take the idea expressed in the code and pay somebody with the appropriate code to fix it.

And it terms of military expenditure $50k is a joke.