I think (hope) they are just describing this wrong, rather than adding bacon to boiling water at the beginning.
The sauce for carbonara is just some of the (salty) pasta water and egg yolk.
Cook the pasta until just before al dente, then mix the yolks and (fried) lardons in the pasta for the final minute or two of cooking. Add parmesan as you like.
You explained this so much better than my attempt, and with a well balanced amount rage ๐ค