She was alert when the paramedics showed up, but the subsequent tests at the hospital proved nothing. The cardiologist, nurses, and other doctors all seemed to agree that it was "nearly a SIDS thing" and that we just got lucky.
After that night, and for every night since (2 more kids since then) we've used a breathing monitor. Occasionally I've noticed the kids will go in a "deep sleep", and the monitor will go off a few times during the night, you'll have to reposition them; they'll wince (in their sleep) and carry on. If that's what it takes, then that's what it takes.
From my research after that event, it seems like SIDS is all-encompassing, and the amount of time allowed for an infant to slip into death may play a factor in it's "suddeness".
I think that's a pretty big exaggeration. "helicopter parenting" usually characterises parents who refuse to/cannot step back from their child's life and let them make decisions on their own. A sleeping newborn child cannot make decision on it's own - the only acceptable form of parenting is helicopter parenting when your child isn't capable of doing anything for itself!
Sudden Infant Death Syndrome exists. You can hardly blame people for wanting to protect their child from it.