A few points from the resident physics Ph.D. candidate:
Quantum tunelling -- the idea that a particle can pass through a potential barrier that according to classical physics is too high for it to cross -- isn't really "new". We're talking about basic quantum mechanics -- i.e., physics from the first half of the 20th century.
Anyway, what you're talking about isn't really quantum tunneling per se -- more like the probabilistic nature of quantum mechanics in general (of which quantum tunelling is one consequence). Yes, there's a chance that a particle that's observed in one position will later be observed in a drastically different position. So, in
principle a bunch of particles could go from one configuration to another due to probabilistic effects. But when we're talking about this happening for all the particles in a macroscopic object (in other words more than billions of billions of particles) it is not only "improbable", but ludicrously, absurdly, ridiculously improbable.
I'm not going to try to work out the exact probability of all the atoms of a human being spontaneously reassembling themselves to make a chair due to random quantum effects -- but I feel confident in predicting it would not happen even once even if you could wait a billion times the age of the universe.
I just want to make this clear -- quantum mechanics doesn't make any prediction that we should see magical effects like people turning into chairs in the real world. Maybe such things are possible in principle, but they're so absurdly unlikely as to make such possibilities meaningless. Furthermore, I know of no credible scientist who believes the basic laws of probability can be in some way altered. In fact, experimental science is dependent on the assumption that the laws of probability are absolute. If your theory predicts that a certain outcome is absurdly unlikely, and that outcome is then observed repeatedly, scientists will conclude your theory is wrong. They won't say "Maybe the laws of probability changed to make that outcome more likely."
I just don't want anyone treating all the bull**** "psychics" and magic acts out there with any more credulity on the grounds that "quantum mechanics says anything is possible".
Of course, in comic books the writers can make up whatever pseudo-scientific B.S. they want.