As for law I couldn't tell you what is right. The "mushroom" is a plug patch I use it sometimes when it's a larger nail or something if it's a very small hole I just use a good old patch. I have heard water can get in the hole and cause problems but have never seen it happen.
As for your second repair when he pulled the patch off he had to buff it to get a good clean spot making that rubber on the inside a little thin.