And Siri only does offline voice recognition and never send sound clips to the Apple for data mining?
"It's not exactly true of all data"
I said that explicitly thinking of Siri. They absolutely send that raw voice data to Siri but in theory the server could only be doing processing, to convert the speech to text and then return you a result.
The question is what is remember from that transaction. Do they use that data to improve further conversions? I would image so. But what I DON'T think Apple does is remember that you personally asked Siri to look for Ice Cream stores at 7pm. All the processing being done on the server though, there's no way to say for sure, except to say that Apple does not benefit from keeping data like that since they don't sell it to anyone or use it themselves .
HealthKit is much more sure - all of the data is from local sensors, locally stored. You don't HAVE to back up anything to iCloud and I'm not even sure it does get backed up there anyway (in fact the more I think about it the more I am pretty sure that does not happen). You can easily monitor, if you wish, what data leaves your device for a while to be sure it's not transmitting anything.