there is no difference between the doctor example and the trolley example save for the intuitions we have about doctors; namely 'doctors save lives'. in your own tailored example, you do something very similar as in the doctor scenario, but in the opposite direction. the new intuition is aimed at minimizing the active element. without the initial passivity, it is not the same scenario. but the intuitions you try to bring in with making it a plane serve no other purpose then trying to muffle that vital element of the scenario; namely that as a given, you do not control the situation. and this is the core of the ambiguity the trolley problem hinges on: there is a situation you have no control over, but you can seize control. that situation is then pressurized by a rational calculus: 3 lives versus 1. purely intuitively; that is, if it were 1 life vs 1 life, nobody would seize control.
I agree that our intuitions about the proper role of doctors play a role, but I do not agree that the rest of the difference is simply one of activity and passivity. In the case of the trolley, or the plane, the choices are very sharply defined, the consequences are very sharply defined, and the circumstances in which the choices present themselves are very sharply defined and very limited. In the case of whether a doctor should be permitted to determine whether healthy x person should be killed so that a, b, and c persons should live, the choices and consequences are not sharply defined at all; and there are few limits to the circumstances in which this choice could occur. Which person will the doctor kill? What are the effects of universalizing this rule of conduct? Given this lack of definition, we think more about the consequences of universalizing the doctor's conduct, and strongly dislike the result. We are less concerned about that in the case of the trolley, or the plane.
Let's take another example, that involves more activity than the trolley car, but it just as sharply defined and limited in circumstance.
You and a group of 5 other individuals are exploring a mine. You all had to crawl through a very narrow entrance. As your sixth friend tries to crawl through, a rock composing the entrance shifts, trapping him with half his body in the mine, and half in the entrance itself.
As you and your friends struggle futilely to free him, you hear a crash from deeper in the mine, and water begins to swirl around your feet, rising rapidly.
Examining the rest of the room, you notice light coming through a high crack in a wall, and determine that by knocking a support beam down, the wall itself will likely collapse inward and leave a space to exit. You and your friends can avoid being crushed by the falling wall by standing on the other side of the room. Unfortunately, your stuck friend will be crushed. If you do nothing, all will drown. As a variation: if you do nothing, you and your five friends will drown, but the pressure from the water will, regrettably after your death, allow your stuck friend to escape.
Now, without simply arguing against the hypothetical (how do you know the wall collapse like so, etc.), what would be the ethical act?
Other possibilities:
A suicide bomber is driving towards a crowded school, with a child sitting on his lap. Your weapon is sufficient to pierce the windshield, killing the driver, but insufficient to stop the vehicle itself. Worse, you have no clear line of sight to the driver; you would have to kill the child to kill the driver. What's the ethical action? How about if the bomber's hostage were an old man? A violent criminal? Your loved one?