The wedding planner is correct. However there are several reasons why you must pursue this. You say in your question that the bride's parents do not want children to attend - did you know this before the invitations were sent out and did you discuss it at that time and if so was there an agreed outcome that you all support?
If you did not know of the other parents position on this and only found out when the invitations had been sent and the call to you friend had been made then you as the person paying part of the bill you have every right to weigh in on this issue.
My suggestion is that the two sets of parents must sit down and discuss this to either express concern that there was an agreement that now seems to have changed or that there was no prior knowledge of their position and this has come as a shock to you.
You need to know if the close friend who was called was a one off or were they are one of many who were called. From your side focus on understand why they did this and based on what you learn then decide your response. Explain that their call caused you and your wife great embarrassment when you were told about the call as they are very close friends of yours.
Good luck with this. If you have any related follow up questions please let me know.