The reason why this might work is the Seventh Amendment, which guarantees a jury in federal lawsuits so long as the amount disputed is over $20.
https://en.wikipedia.org/wiki/Seventh_Amendment_to_the_Unite...
> In Suits at common law, where the value in controversy shall exceed twenty dollars, the right of trial by jury shall be preserved
If Google says "yep, we're not disputing that we owe the federal govt $1 million, here's a cheque for that amount", their argument is that the "value in controversy" is now $0. Since $0 is less than $20, that clause doesn't apply.
I'd like to hear what an actual lawyer has to say on the odds this'll work, though.