The option that's fee-free to users probably costs more for the city, whereas the ones that charge a fee will probably be cheaper or even free for the city.
A city council member trying to balance a budget isn't engaging in corruption by choosing the option that reduces an expense in the city budget, even if it just places the cost on the people paying for parking instead. Constituents would be more likely to complain about higher property taxes or cuts to city services than to complain about a fee like this.
Maybe they just got bribed, but that seems less likely.