An hungry dog is not to be joke with, dog's will do whatever comes it way if someone makes it angry, humiliation is very bad for a person to involve himself with, respect is the peace we need to embrace.
Those people were right to blame the incident on you, it's doesn't seems nice to be treating max that way, show him the love he deserves, and it would be good to you too.
About the mud, do not worry water and soap is going to wash it away for you.