In this particular case it was "The blood of the covenant is thicker than the water of the womb"
First explanation I heard was that it meant that the bonds you make in life can matter more than blood relations. I was talking with someone and they said it was a biblical thing though I forget their exact phrasing.
I can't recall ever hearing the religious take on it, but I HAVE heard the "blood brothers" interpretation of it. You sure the second person isn't wrong? :V
In fact, if where I heard that reference was correct about the phrase originating in ancient Greece, that increases the odds of it being being biblical in origin.