OP, I think you're looking at it in somewhat the correct way. The way valuations are determined are by normalizing everything. Thus, if you and a neighbor had exactly the same size and type of lot, cookie cutter same house with no differences inside or out, they'd be valued the same. If your interior was updated 2 years ago for $50k and your contractor took out permits, they know this and will add to your value. I applied for and received an abatement shortly after moving into my present house. I took all the comps that were used in the sales material and applied the standards. House #1 is the same age and size as mine but has a 2 car attached garage and its tax is lower than mine. House #2 is larger than mine with a finished basement where mine is unfinished and it has a lower tax than mine. Out of 10 comps, I used the 5 that would support my case.
But yes......they can increase your tax. If you tell them that the neighbor's house is exactly the same in every way and they come out and look at their house and your house and find the neighbors still have the olive drab colored kitchen installed in 1972 and you have a fashion magazine kitchen, rehab'd a year ago and both of you have the same tax, guess what? You lose and pay more.
Good luck, but you will really want to make a solid case and ask for reasonable changes. In my case, I did just that and won. While turning in my application, they looked at it and said it looked reasonable, then told me about other people who challenged their taxes every year and submitted nothing to support their claim and were denied every year. Don't waste their time if there isn't really a mis-match in valuation compared to another house.