Kosher Loopholes?

I was with family in New York who are very Orthodox and strictly kosher, so I was very surprised by what I saw happen in their house. They were cooking meat on the stove and one of the children accidentally dripped a couple drops of their ice cream cone into the pot, which I would have thought would have made the whole thing non-kosher. But my cousin, who is very strict about everything and studies Torah every day, came home and said it’s ok because not enough dripped in to render the meat not kosher. I didn’t want to say anything, but it seemed very self-serving; how could he decide that it’s “not enough” to make it non-kosher?! If G-d said meat and milk is treif, why would this not be treif?! Am I missing something?
I would appreciate your answer because this has really been troubling me; in my mind it calls into question their integrity in all they do.