Talking to professors without attending that University
Okay, so this might sound a little bit too honest.

You can email them, and if you're sufficiently interesting or intelligent, they will write back. For example, if you asked things like "what is the best sorting algorithm? Can you explain why that is?" they probably won't respond, because it's boring. You have to realize that the professors usually also get a lot of "crank" messages (false claims to amazing results) to which they don't respond to. However, if you actually read and understood their research, and had something that you could contribute to, then they probably will respond. Your pedigree isn't extremely important, as far as I am concerned. It is true that the top scientists are available for free, but only if you are worth their time.

The university system requires the professors to talk to the amateurs that they normally wouldn't talk to (i.e. students). My university had a student who claimed to have proven P vs NP problem. Normally if someone sent me a proof of that by email, I'd have deleted it without reading it, but since it was a known student, the professors still looked over the proof (it was actually quite clever, albeit wrong), and the student was eventually offered a summer research position. So I wouldn't say that the university system is pointless.