Hedging can be a motive for trade, and if the bet event is correlated with one of the few market "factors" that have risk premia, then the market probability for that event will weight high risk states differently. The prices can still be informative then however, and most claims don't correlate much with any of these factors.
I'm confused about your point re betting prices. If the outcome of A is correlated with other valuable things e.g. stock market prices, then betting on A can act as a hedge, distorting the price away from the underlying probability.
Hedging can be a motive for trade, and if the bet event is correlated with one of the few market "factors" that have risk premia, then the market probability for that event will weight high risk states differently. The prices can still be informative then however, and most claims don't correlate much with any of these factors.
I'm confused about your point re betting prices. If the outcome of A is correlated with other valuable things e.g. stock market prices, then betting on A can act as a hedge, distorting the price away from the underlying probability.