Zestimate NOT ACCURATE

Zillow does not change Zesitmates by request, but there are things you can do as an owner to make you home page more accurate. Make sure that you have claimed your house and edited all your home facts to be accurate. Not edits affect your Zestimate, but some do so it's worth doing.

You can also make a note in the owners comment box about your feelings about the Zesitmate and also explain features that Zillow has not included in their numbers. That is a way to communicate directly with people that look at your home page so they can see more than just that one number from Zillow.

Zillow publishes data on their tolerance range:
Zestimate® Values & Accuracy
and
by County Excel file

Zillow doesn't offer the kind of "accuracy" you are asking for.  It is only a machine generated opinion of approximate value based on public records data, owner/agent modified data, and recent non-distressed sales in the area.

Each estimate is done individually by the machines without regard to the estimates of neighboring properties.  If what you claim is "true", then your neighbor's estimates are just on the high side, and yours is "right".
Also don't forget to look at the estimate range given, as that is usually more meaningful then just one number.

The last sold price adjusted for last sold date has a major role in determining the estimates.  So does the tax assessed value adjusted for local tax rules.

If you need more "accuracy" than Zillow offers, you will need to pay for an appraisal.

You can also check out the machine opinion of approximate value offered by some other "free" sites for additional comparisons:

Homesand.net

Eppraisal

realquest.com express

cyberhomes.com

trulia

chase

homegain

homes.com