What this question comes down to is the usual "realism vs gameplay" argument.
Yes, elite soldiers missing like that is somewhat unrealistic.
Yes, elite soldiers battling turn-based is even more unrealistic.
I dont' know if the story is just as unrealistic or slightly less, tough call. Nevertheless it's extremely unrealistic.
In game development gameplay is always more important than realism. However, depending on the details involved, realism can improve gameplay - altough often it does not. Currently the miss chance is intended make the game more fun. If soldiers would always hit and the aliens had more hit points it would make the game simpler and probably less fun, because you know you have to shoot an alien exactly 3 (for example) times before it dies. The miss chance brings a kind of action to this turn based game.
Right now you can miss and by taking a risk and moving closer you can lessen the chance to miss significantly, or you can hope you're lucky.
I've had multiplayer sessions where a soldier missed three times in a row, and despite being somewhat humiliating it was fun (damn stupid bastard, hit, him, HIT, damnit..). Of course it's even more fun if the enemy comes around the corner, you've got 10 hp left, he shoots, misses and is out of TUs (and it's his last soldier *evil*)