Only a controlled economy can be spared from inflation (though this is also debatable)....
It is a known fact that inflation has no business with bitcoin. Inflation can be in a controlled environment as you have rightly said and bitcoin is not controlled.
There have been many discussions -- continuing discussions in fact -- on this subject and still there is no definite answer maybe because Bitcoin is still relatively new and theories/speculations are still waiting for validation.
Yes and I wonder the kind of hypothesis or theory that will be pushed in to invalidate what we already know and experiencing - that bitcoin is not inflation prone but rather, bitcoin can cause inflation because high rate of bitcoin price might mean too much money in the society when converted.