[makeitdouble]

The trolley problem is specifically about a situation that is ongoing regardless of your presence.

You're not running the train, nor own the railway, you didn't bind the people on the rails. You just happen to be there, and can perhaps improve the outcome.

In case the worst outcome happens because of your inaction, the biggest moral fault lies on those who created the situation in the first place. (If you're looking at a bank robbery and don't push the alarm button, you have some moral responsibility, but the robbers are the villains.)

When you take action, you become part of the situation and take full responsibility of the outcome.

So, no, I don't think the choice are morally symetrical. Taking action is morally a high risk high return strategy, while inaction is low risk mild returns (best case is you did nothing and that was the right choice, so you could have been absent, it wouldn't have made a difference)