No, that is not necessarily true.
If you are 65 or older your residence homestead qualifies for more exemptions which will result in greater tax savings. The amount of the exemptions that are granted by each taxing unit is subtracted from the market value of your residence and the taxes are calculated on that “lower value”.
In addition, when you turn 65, you may receive a tax ceiling for your total school taxes; that is, the school taxes on your residence cannot increase as long as you own and live in that home. The ceiling is set at the amount you pay in the year that you qualify for the aged 65 or older exemption. The school taxes on your home subsequently may fall below the ceiling. If you significantly improve your home (other than ordinary repairs and maintenance), tax ceilings can go up.
For example, if you add a room or garage to your home, your tax ceiling can rise. It will also change if you move to a new home.