I think that the overall list of 'fastest companies to IPO' might be skewed by the dot-com bubble companies that were fast to IPO but failed soon afterwards thanks to having no real business model or income.

Not that I know of. Although it would only be non-YC companies (no YC company has IPOd yet - Dropbox and Airbnb are the likely candidates but Weebly has also hinted that they might be in a position to consider it soon)