Google penalizing websites for gaining backlinks to fast is just a
SEO myth.
If that would be true, everything that ever went viral would be banned from SERPS in the matter of hours, but we can see that's not true.
Google will never penalize a website for the links it can't control, the links from other websites pointing at it. This would allow you to remove your competitors from SERPS by building lots of bad backlinks to their websites, now wouldn't that be just plain stupid from Google?
Google will sometimes neutralize the value of a backlink if it finds it spammy, but it will never penalize you for it.