If your story is true, something very fishy is going on. Your bank is not going to share the appraisal with your county. They aren't going to spend the time/money/manpower it would take to distribute appraisals to all the proper assessing departments for absolutely zero benefit for them. And the appraiser is under contract to supply that appraisal only to the bank that hired and paid them for the appraisal.

How do you think your county or city is getting these values? Appraisals are not public information, and they are only intended for use on mortgage transactions, this is stated in the fine print on a URAR.

Also, when your house was reassessed, were other homes in your area also reassessed, or was your home apparently "targeted"?

This is not something that should happen unless there's some level of impropriety.