I have heard that explanation, and it could possibly mean exactly that.... except when a baby is born, it is not normally said that the baby was "born of water"..... they were simply "born".
Jesus could have been hinting at the water breaking during a human birth, but he also could have been using that hint to say "not only do you get baptized in water, you also will be baptized in the Spirit...... because remember, again, anytime anyone during that time said "baptism", it always meant immersion in water. (unless they were discussing making pickles...
)
It would be similar to the comparing of water immersion baptism to the "saving" of Noah and his family..... "baptism, which corresponds to this (Noah being saved from destruction by water) now saves us.... " Noah's family was saved from degenerate earth by the cleansing power of the water....