What extraordinary tactics by the school!
If our son's school threatened to kick out every parent who has ever said something "nasty" about a teacher, they would lose around 90% of their pupils and thus income. Likewise I can't count the number of times people have discussed openly that they have been in to complain about a teacher. Most parents have issues with a teacher at some stage in their child's time at any school.
I have always said to the nicest teachers that they can be sure they are doing a good job because their name never comes up at the school gates!