OK bear with me, I'm going to lay out an example to make sure we're really on the same page:

Suppose I am a horse racer in a two-horse race and have been paid to lose, so I know that the odds are 100% on the other guy. 100 people place bets of £1 each on each of us, believing we're equally matched, so there's £50 on me, £50 on the other racer. The bookies will now be offering evens odds - less their take - on each of us. Suppose now that another 100 people, tipped off by the racer fixer, place bets of £1 each on the (known) winner, so there's £150 on him, £50 on me. While this is going on, the bookie adjusts the odds so that what they offer is more like 3 - 1 for the winner.

The odds the bookie offers change in accordance with the bets placed by the punters, even though the actual odds of the race never changed. This was due to the the bias of the punters. If we re-ran the experiment but the punters instead for some reason believed I was likely to win, the bookies odds would reflect that biased belief - a bias that would then be incorrect rather than correct.

So, assuming you do agree with all that, where do we actually differ? My point is that while, sure, "people don't win money by getting their bets wrong", you can't rely on the people betting to be correct. "But FishFace" you may say, "you can rely on people in aggregate to be as accurate as it's possible to be! You can't beat the market!" And I'd agree with that too, so here is the crux: the people placing bets are not "the people in aggregate". The people placing bets may have some bias not reflected in the population as a whole. The bookies cannot correct for this: it only evens out the risk so the house always wins. If the bias is like people acting on a tip-off about a fixed race, they'll be more accurate than the general population. But if the bias is, for example, smart people being less likely to gamble, and smart people being more likely to think a particular outcome is likely, you might end up with bookies' odds being less accurate than the general population.

There's another confounder, which is the concept of emotional hedges where people bet not according to whom they think will win, but so that they get some money if their preferred outcome fails to materialise. Bookies' odds just fold this into all the rest of the bets to produce odds. But if for example a lot of people in favour of this bill emotionally hedged, the odds would say it has lower chances of passing than it actually does.