The rule says that you can overrun 1st base without liability to be put out as long as you return to first without making an attempt to advance to second. But this is in the umpires opinion. What happens is you get a poorly trained umpire, who hears that you have to turn right, and he makes a bad call.

I think the rule is you can over run 1st base but you can't make the turn to 2nd. If you turn, you can be tagged out.

You can turn anyway you like as long as you don't make an attempt to advance to 2nd. the problem as stated above is that attempt is based on the umpires opinion. We teach out players to break down after the bag look over their shoulder for the ball and then huslte back to the bag.

The only way to be out at first when over run the base and take a turn left, is if the first baseman tags the runner before she gets back to the bag

What the others said is correct...without an attempt, they are supposed to be out of jeopardy. However, it's always "safer" to turn away because not all umpires will see it the same way you do or the way you intend.

if you go by how the umpire sees it, its probably not good. stay in foul territory, break down and look to see if there is a past ball. do whatever you can to keep the game out of opinion by the umpires.