Hey, That's All True...
...but, it sounds like the screw is already fubarred. That's a good point, to head off the problem before it starts. Use the right size screwdriver in the first place, and make sure its tip is in good condition. Heck, make sure you're using a good screwdriver in the first place. If you bought a set of eight screwdrivers for five dollars at the the local grocery store, chances are they're not made of the finest, tempered steel.
Also it's a good idea to see if the screw head is free of debris. Blow it out with compressed air if need be. If the screwdriver doesn't seat in the bottom, you're off to a bad start, and possibly a rounded out head. Lastly, it helps to bear down hard from the start, and make sure it doesn't start to slip in the first place. Once it starts to slip, it only gets worse.
But, that's all moot for thekirbylover. Hindsight is 20/20...