I actually had a lengthy battle that I won with the Berkeley County Assessors office last year.
Brief of the story:
-Couple that sold me the house bought it for $X in 2007 and shortsold it to me in 2009 for $Y (Y= X - 30,000)
-Pre-closing appraisal came in at $Z (Z = X - 17,000 or X + 13,000)
-County wanted to tax me at $X and was taxing me at the 6% even though I turned in my paperwork.
I sent a letter appealing the decision. They denied it.
I had several phone conversations both with my assessor and her boss the head of the department, he hung up on me on at least one occasion.
Sent in for an appeal in front of the appeals board. That got scheduled and I sent in all of my supporting paperwork and a letter explaining my whole case.
The day after they received all of that the original assessor contacted me to let me know that they had reviewed my case and agreed to tax me on the pre-sale appraisal amount.
Also turned in my 4% paperwork (again) and got the reduction there.
A couple of weeks later my mortgage holder got a refund check for almost $2000 from the overpayment and my monthly payment only went up $9 per month instead of $200.
Long story short: if you have a case, appeal it and don't let up on them. You will probably not get the 4% unless the home becomes your primary residence but if you are arguing the value of the home then by all means contact them and see what happens.
Edit: I spoke with the Real Property Office not the Assessors office. The department head there is Wilson Baggett.
Here is a link
http://www.berkeleycountysc.gov/dept/realproperty/