I didn't get a Best Time, but it said I did

I guess the computer just likes you.

Actually, it was probably either that you reset the high scores or you made less mistakes than the previous version. If mistakes are allowed, someone who takes longer but makes less mistakes is better than someone who takes a shorter amount of time but makes lots of mistakes. This is to prevent someone who sets the number of allowed mistakes really really high and then clicks on each square really really fast from getting a better score than someone who actually played the game.

You can't correct this by not entering a name, since it saves the high score as soon as you get it. If you really want to fix it, either reset it or remember or write down the old high score and see Correcting your best times.