This example demonstrates value of asymmetry of information when making a deal, but not "don't make first offer" principle. Obviously the lady was ignorant to the true value of the balls, as any non-golfer would.
It wasn't that she had a lack of access to the information (IE a non-golfer randomly acquiring the balls), he husband was an avid golfer and she said her son was semi-pro. She simply didn't care to get the information before selling a product, which is another lesson entirely.