You already know the answer. The SCOTUS decided to hear the case (which they did not have to do), and they overruled the Florida Supreme Court (which they did not have to do).
If the SCOTUS was just a little bit more Liberal, the Florida Supreme Court would have prevailed and Gore would be President today.
Even though it's the business of the states, the US Constitution is whatever the SCOTUS interprets it to be at any given time depending on the prevailing ideology of its members.