Translation:The apple falls on the newspaper, not on the ground.
I'm fairly certain we could replace "onto" with "on" here and not lose any of the meaning in English. In fact, I think saying "onto" is a little awkard. Am I missing something, or does this seem correct?
As far as Hungarian is concerned, you are not missing anything. If it sounds more natural that way in English, then please report it, it should be accepted.
You could but i would rather see the legitimate onto here.
Fall already implies a direction, so English allows the removal of the to part, but especially when it so nicely mirrors the Hungarian meaning it is rather unfortunate that now the solution is really on. Not wrong though.
I myself (American English) do not find 'onto' awkward, and I think it better conveys the idea of motion. It is true, however, that many speakers do say 'on' when they mean 'onto' (and 'in' instead of 'into', etc.)