Just because I spend money on something, does not mean that I produce that thing, even if my spending increases demand for said good. That results in double counting production, which was already counted once by the seller.
I'm not focusing on what is produced (in fact, I made an explicit statement to this effect), but on investments made that drive productivity growth (which is considered the most direct driver of economic growth). And if those investments made earn more than the costs of interest on the debt, then it's a net win for society.
The part of the trillion dollar injected in any economic activity in a closed system stays in that system.
(The part of that sum that is used to buy imports is another thing, although I guess it's far more complicated to properly account for)
Honestly, every time I think about this my mind just melts; I'll be really glad if somebody can clearly explain where is the catch.