So few candidates so rarely have the power to negotiate above what the hidden range already is, that this is a non-issue.
We really shouldn't be deciding policy based on the outliers, besides which those people (the outliers) that can dictate a number higher than the range already set aren't hired from advertisements anyway, making the whole "but we can't do this because it would affect those who don't apply respond to job ads"...
You are allowed to hire whoever you want. How could you come to your conclusion? You are allowed to hire people without making job ads at all, for that matter. You are allowed to hire 10 people for a position even if you only advertised 1. And of course you are allowed to pay more than initially advertised.
Says who? No one is saying you aren't allowed to go over the advertised range.