There is such a thing as over apologizing and doing so almost makes you guilty. It sounds like you over apologized which put you in a position of seeming guilty.
When she brought it up, all that needed to be said was "i'm sorry, I wasn't aware of this situation I will speak with my child about it, thank you for bringing it to my attention." end of topic. By going on and on about not knowing, their child never told you, your sorry etc...it makes the whole situation seem bigger than it is.
It does sound like your daughter has been acting poorly at times, and that she may have been acting poorly in this situation and yes it needs to be discussed. BUT she is 4, he is 6 and she was being silly. I mean, I am chuckling at his "I have a secret, lean in pssttttt" (or what ever the tongue out spitting sound is) hahahaha that my friends is classic childhood. As adults we use it as a teaching moment that it isn't appropriate but it is silly childhood behavior. Obviously if it is persistent and is being done with a mean streak to it then we need to act even more firmly.
The parents needs to figure out what exactly it is that is bothering them as it likely stems deeper then this incident. In the future you need to be confident, apologize once, note you will take care of it and leave it. If they keep trying to go deeper and put you in a position of weakness end the conversation, a simple..."I'll go speak to her right now" - click. Have you child write an "I'm sorry" note or some other notable apology for the parents to see if you think it'll help them.