According to another website much like this one, somebody sternly warned a fellow member not to sleep in their daily contacts because their eyes will "grow over them" or some such nonsense.

Here at Lens 101, you can be safe from that sort of foolishness. It's a very bad idea to sleep in daily disposable contact lenses, but not because of anything growing over your contacts and sealing them to your corneas forever and ever. Such things only happen in bad movies.