What Gives Anyone the Right to Discipline my Child?

I know many of us have been in the same predicament. Whether at someones house or  a public place; somewhere at sometime we've all witnessed and a child is misbehaving.  This is a very tricky and challenging quest for most. Often there's a fine line. Most of the time we bite our tongue and pray for the parent to step in and discipline their own child.  On occasion, and I say this with extreme caution, I have had to ask a child not do do one thing or another. Most likely the child may have been in danger or put others in danger.
What do you do when other people try and discipline your child and your right there? Have you ever had another person spank your child? If so how did you handle it?
On the other side of the coin... When you try and discipline your child does another person interfere by undermining you?
I personally believe it is not any ones right to discipline my child or to yell at them when I am there. I do acknowledge that I may not always be available. In the extreme situations where Discipline be necessary and my presence is not available a simple time out may be warranted. However, hit my child and you will be dealing with mama bear.
What are your past experiences and feelings?