Ours definitely reproduce as described. Our oldest shrooms are still under a year and they repro, but slowly for us. My guess is that once they've covered a rock, then they'll spread elsewhere, preferably to a well placed rock to share with friends or possibly a little cash back from the LFS.
We just got some green shrooms and 6 hairy shrooms bout amonth ago, so they havent done anything yet. Heard that hairy shrooms split, true?