@GApeachy... there may be other methods insurance companies can and likely do utilize but a tax basis may not accurately reflect what the real cost of construction or replacement is.
In Minnesota the State oversees all assessing with the County serving more as their local agent. Some cities use their own assessor that still reports to the county. The county reports to the state. Now the assessor establishes an assessed valuation based on formulas provided by the state and that factors in valuations of similar property sales in your local community. The local government (community or township) has to keep the value of a property within 90% to 105% of the values as determined by information from the state and county for certain classes of property (residential, commercial, industrial, vacant land etc). In our state, generally the property assessment is based on a previous three year rolling average and is LOWER than the construction cost values. If the state is not satisfied with the local assessment or what the county has done they do step in and order value changes.
Real life example is: a house that has an assessed value of $93,000 has an insurable value of $150,000. This is example is real.
Now there are other rules for insurance that due effect a complete recovery on a property loss (or it used to be). Your insurance limits had to be within 80% of the insurable value NOT the assessed value.
One last comment now that you have become an expert in property assessments ... other states may use different methods for assessing and insurance companies vary on how they may determine your property values so this would be a conversation with the insurance company! Bring you back to when setting your value for insurance values on the property, I have seen it where companies use 90% also. Why they don't all require 100% is (I can't recall) a question?
(now go play with a spider in a corner, you're really being badder than usual mister!)