Your idea that everything that is not given a sufficient technobable explanation must work by magic is an odd one. And no, I am not going be able to prove to you that this is not the case any more I can prove to you that prayers do not work. I just have to wonder why the hell would you think that.
And comparison to Star Wars is actually good one. These two franchises have marked difference in tone. SW is more of a fantasy story set in space whereas Star Trek has always been a pure Science Fiction series, albeit rather soft one.