Risks to Recording...? Can I be detected and sued for capturing streaming lectures?

This might be a really stupid question, I'm new to this... but if I record a streaming video, can the website detect what I'm doing?

I'm taking some University courses, I don't think they want you downloading the streams, and it would suck if they end up blocking me, or suing me because I was recording the stuff.

Anyway, might be not be the best question... but I'd appreciate any advice.