Freezing Water To Make A Mikva

I was really surprised by this. I knew about the Mishna in Mikvaot that says snow and ice can be used for mikva waters, but I always took it as a foregone conclusion that that's barring any original psul of מים שאובין i.e. it just fell from the sky that way and you then transport it to the mikva. But to take already invalid מים שאובין and make it valid by way of freezing-- that I thought was crazy.

Then I looked up an Aruch HaShulchan (סימן ר"א) who brings from an explicit Tosefta (טהרות פרק ב) that freezing even removes the פסול שאובין! Frankly I'm in a little shock primarily because it runs against my whole sense of "coming-into-existence" theme of mikva that I had developed על פי דרוש. Particularly two points:

1) הויה על ידי טהרה - surprising that something demanding a concept like הויה על ידי טהרה would allow for just a freezing and thawing of an already extant invalid body of water. That dissolving would be seen as a new הויה I don't hear.

2) the sense of לידת\הויית גשמים -- see Bereishit Rabba 12:7 מטר יש לו תולדות, שנאמר (איוב לח): היש למטר אב -- I had assumed it was this element which was part of the effect of Mikva. The rebirthing. A new existence...

So I guess the upshot is that I'm wrong. :-) So be it.