If we look at this from a game theory perspective it actually works in their favor. People want to make lots of money, if they lie they're going to lie about being paid more and not less. If enough people lie to affect the overall statistics, then everyone is going to be pissed off at their management for not getting paid as much as everyone else. At this point management has two options: reveal the actual salaries of everyone, to prove that actually everyone is getting paid less than what the stats show (oof), or keep the salaries hidden and deal with a workforce in which every participant believes they are chronically underpaid. Neither of these options are good for management, and the only way out is to hand out generous raises.

Or, claim the entered compensation is not accurate and maintain the status quo.

Right, but that's the expected response. Of course the company is going to claim inaccuracy. It doesn't grant them any more credibility than they would already have if it turns out they are actually right. Another point for the organizers.

They can fire one or two people who put their salary on the form.

They can say that it's because they lied and cannot be considered trustworthy and just hint that there are others.

Strictly speaking telling the truth should be protected, but the backlash would probably inhibit that too.

Especially if the goal of this is to pressure management into increasing pay, people will absolutely lie, if only to stir the pot.