That's not actually true (according to Wikipedia and a few other sources, at least). The 'blood is thicker than water' saying has been around for centuries in various forms with the current meaning, and the covenant/womb variation is relatively recent, and mostly stems from a few books that claim that it's the 'real meaning' without sources or proof.
Thank you so much for saying this! One time there was a Twitter thread that started with someone asking, "What are some things that people believe/accept without having liked into it further." Someone responded with this "the original phrase is... covenant...womb" and the OP replied with someone like, "yeah people are such sheep". I wanted to explode.
But to back your point, you can go and read for yourself the very first instance of this phrase in context as the very old book it comes from has been digitally scanned. It's old enough to be in middle English, but I still thought it was fairly easy to make out the original phrase as we know it today.