Dear how wide a scope?
Your inquiry is mostly political because the issue you framed is how localities interpret New York State law. When a person becomes aggrieved by the actions of a town, acting through a board, the general method to challenge the legality of the action is by means of a lawsuit brought under Article 78 of the Civil Practice Laws and Rules.
Read more about the Article 78 proceeding at:
If the political issue affects a number of persons similarly situated, the could join together in a group with one attorney to challenge the process as contrary to law.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.
Perhaps I'm naive, but one would think the information required challenging an assessment woud be relatively straighforward for a residential property appraisal: inquiries into fair market value based on comparable sales prices, purchase prices and physical characteristics of the building, whether you are 65 or a veteran or not. Much of this information would either be from public sources or not terribly intrusive of privacy.
For commercial, industrial or income properties, however, I'd expect there's some right under certain circumstances, if an assessment were challenged, the Board and Assessor could inquire into income, expenses, rate of return and other financial information of the revenue streams from the property, because that's one method of determining value. Is that what you're referring to?
Can you please give a better example of the intrusive information requests you're mentioning? Not enough information in your question to determine an answer, or even what your complaint is exactly.
You should write your congressman. Everyone is frustrated with rising property taxes, but the bottom-line is that irresponsible fiscal spending by government bodies and stagnant real estate values combined with diminishing state tax/local receipts tent to lead to increased property taxes. This is a fact of life. The best way to change the status quo is to become involved in government policy and advocate for changes that will correct this problem.