Rinky-dink (non-Berzerkely) universities do this by setting configuration options in the registration software such that only a certain number of people can register each semester. If you get in a bit late and have a transcendentally good reason to need that course that semester, the professor is allowed to sign a small form which overrides the software and lets you in anyway.
In short, unless UC-Berkeley's software is stuck in 1968 just like its politics, the reason you gave is highly unlikely.