I've received a Hungarian Schengen visa valid for 1 year. At visa appointment centre I was warned that to prevent Schengen visa rejection in future I shouldn't enter Schengen area from other countries more times than from Hungary. Is there official source or empirical statistics on that?
Such a rule does not exist.
You should normally apply for a Schengen visa from the Schengen state that is your main destination, which most often is where you will spend most of the time. If you eventually spend little or no time in that state, the reason for applying from that state or even the justification for the trip may be questioned.
If you have completed the trip, reasonably in accordance with your original application and your visa remains valid you can use the same visa for additional trips. There is no requirement for these trips to be to the visa-issuing state.
You seem to have travelled as planned and have kept Hungary your main destination. For your following trips on the same visa, main destination is not relevant.
In any case, this is about time spent, not about number of entries. Passports are stamped when entering and exiting the Schengen Area, not when travelling directly between Schengen states. If travelling to Hungary with a layover in another Schengen state, which would not be unusual, you would not get any Hungarian entry stamp, which would be perfectly in order.
Whoever told you that is spouting rubbish, and should be properly trained or fired from their post.
For the first trip, the main destination needs to be Hungary. That's it; all you need to care about is not spending more than 90 days per 180-day period in the Schengen Area.
So you're all good.