I had a first gen go wacko
In between the late night false alarms my wife cooked something and managed to set off the other, non-Nest smoke detector in the house, which is upstairs. The Nest remained silent throughout.
I called Nest support and mentioned that fact, at which point the support person on the other end went silent for a moment, then said "oh", then offered to send me a second gen detector free of charge.
Since then it's all good – no more 3am false alarms. Just a monthly email from Nest saying no alarms – false or otherwise – this month. Which I already knew, but hey, that email is extra reassuring, since it came from Google/Nest's finest oompa loompas.