It's not clear to me from the article what this looks like legally.
It says the men adopted the children, so does this mean there are two birth certificates, one for the birth parents (whoa are also three it seems, egg donor, surrogate/carryer, and father though I doubt they'd include all three,) and one for the adopted parents?
If so, I don't necessarily have a problem with a second, adoptive birth certificate as long as the one with the biological parents also exists.
But I don't think there should ever be intentional false original birth certificates. They should have the people believed to be the real biological parents, so long as they are known or thought to be known, and it should be possible to challenge them on the rare occasion where it turns out that, say, the father is really someone else.
Birth certificates aren't there to validate the people who raise, or even commission, the child.