If he didn’t pay the bribe there would have been nothing to report.
If they're applied in an unequal way, of course that's different.
As a stupid but illustrative hypothetical example, if the official decides each morning whether he will approve all CCW applications he sees that day or none of them based on a die roll before leaving home, and then unilaterally changes it a month later to go based on whether the last digit of the local CBS affiliate's high temperature forecast from the 7am newscast is odd or even, these stupid rules and rule changes would be completely compliant with the equal protection clause.
I don't believe the legislature has to specify the criteria used, if they explicitly give the local officials discretion, but their criteria do have to have some rational objective.
(How do you tell the difference? Well, as in this case, usually people leave some sort of evidence, and the legal system has a process for demanding evidence and evaluating it. It's not perfect, but it's certainly not unenforceable.)
I'm in a similar situation, actually. I had a trooper lie in court and even admit to it in the complaint investigation, but the investigator (another trooper) said it must be a misunderstanding. I'm curious how intentionally lying to cover up your mistake (exculpatory evidence) is a misunderstanding as a civil rights violation under Brady v MD, but I also don't want to get 'suicided'.
The part which is subjective is deputized to instructors, and one can shop around for a willing one.
The moral hazard you're alluding to is completely absent.
Personally, I chose to live in shall-issue states.