Well, a diesel always runs lean anyway, since there's no throttle - you only adjust how much fuel you squirt in (in the N/A case). With a petrol engine running at the sort of AFRs that diesels run at you would melt the pistons for sure, but diesels handle it just fine. Thus it is at least plausible that there is enough margin for error in there to exploit to find the gains in both bhp and mpg figures. Whether that is what the "box" really does I have no idea - but conceptually, the possibility shouldn't be pre-emptively dismissed.
And yes, I probably read too many books.
And yes, I probably read too many books.