It is well established by John the Baptist that to be born in the spirit is akin to being baptized in the spirit. And I recall Paul talking of the baptism of death and rebirth.
So if we assume then that being born in the spirit is different words for being baptized with the spirit, then here Jesus is saying that both are necessary.
But I of course prefer your interpretation that man is born both of water and of spirit, as you did not object to my characterization of Jesus first being made flesh (assuming that is what being born of the water means) and later his spirit descended into the fetus.
If you believe that characterization, then be careful, for it means that the body and spirit of a person are separate-- Which means that bodies need not be resurrected for the spirit to live on, and perhaps enter another body.
The concept of resurrection is ancient science. You may claim that God can do anything, including reassemble the particles of one's body that may have migrated quite far via microbes and erosion and the like. God would be breaking his own law of entropy to do this, and to do it for all peopls at once. What if the same particles were used in different bodies over thousands of years- a very likely case. Would God then produce duplicates for all bodies. It would be easier just to remake all those bodies.
So please give up antiquated science for modern science. God does not create everything in a few days. God is a minimilist just as nature is. God expends the least amount of energy possible to make things happen. For example, most of the time, he just tells us what to do, both you and me, and lets us expend the energy. Then over millions and billions of years, he gets what he wants, more consciousness and intellect to feed into the Godhead.