Here's the difference - Rolex will not correlate the serial number to the model number. This leaves their customers and potential customers in a position where they cannot tell what model reference a specific serial number pertains to, so very much open to fraud.
Omega is quite different - anyone with access to the Omega Extranet can simply enter the serial number of a watch, and see what reference number is refers to. I do this for people daily - some days many times per day. You can also just call Omega with a serial number and ask them to do the same.
This is how I tell people who are considering buying that limited edition Mauri or Mitsukoshi, that it's either a genuine LE or just a conversion watch that has the dial and hands changed on it. It's also how I can easily tell that a men's Seamaster someone might be wanting to buy is fake, because the serial number comes back to a ladies quartz Constellation. The fakes never match, at least not any that I have searched in the last nearly 20 years...you can't broadly apply what might be perfectly accurate to one brand, to all brands.