Of course flooding can happen to a carbureted engine. It just happens in a different way (over priming, over pumping the throttle (I think, I've never really pumped the throttle in an airplane), etc.).

The Lycoming engine has little tiny fuel lines running from the fuel metering unit to the engine. If you start the engine with the mixture in, you're flooding the little lines and the engine with cool liquid fuel that will not easily ignite. Starting it with the mixture lean ignites the fuel/air mixture, while excess fuel is recirculated.

Don't worry overly about this...other fuel injected engines (Continentals) are started in the full rich position. I think it's just important to know and practice the proper procedures for the airplane you're flying.