Your statement that placing bets does not affect the outcome is true but I don't think you draw the right conclusion.

If markets don't capture current sentiment accurately then bet against every news item.

Let's say there's a market for a coin flip, and periodically, news comes out that makes the market lopsided (one way or the other). You should trade against it. Every time. If you are correct, this strategy will win on average, until the true breakthrough news item, which you'll be on the wrong side of. Just don't keep doubling down, because the final trade will be the one you lose.

This will demonstrate who has "deduced a more accurate prediction". Everyone else put together, as events unfold, or the opposite of that.

*changed to will win on average.