Sorry to chip in after you said this was all for Luksy, but I had a gander at those questions and the first one does have (very flimsy) context within the original game that might help. Basically, Shinra are actually spinning the accident as having no casualties because of their 'quick response'; this dialogue comes from the TV in the Turbo Ether house of the slums:
“This just in. An accident today…”
{NEW PAGE}
“…the worst in the history of the metropolis.
But thanks to the quick response
by those in charge,
there were no civilian casualties.”
{NEW PAGE}
“The cause of the accident is still unclear at
this time{, }however{, }according to some
sources it is believed to have something to
do with the terrorist
group{, }AVALANCHE.”
President Shinra mentions this 'plan' in the scene just before the sewers, when he says this to himself:
President Shinra
“We'll destroy Sector 7
and report that AVALANCHE did it.
Then we'll send in the rescue
operation care of Shinra{, }Inc….
Heh{, }heh{, }heh…this is perfect.”
So the context for Heidegger saying 'after all, we're the ones who saved Sector 7 from AVALANCHE' is that he's alluding to Shinra's propaganda spin that they saved everybody from the dropping plate. His original line implies they saved the actual sector though, rather than just the people.