Can you explain this to me? I don't know what any of this means.

Consider it related to the Streisand effect or reverse psychology concepts.

Except that only his character was Streisand-ing it; Colbert-the-person thought it would be hilarious to slyly encourage people to remix a spoken interview with a "great dance beat" (and, at the time, it kind of was)

I think he is equating stern copyright notices to somebody making a strong statement about what annoys them. As if to say “so what”, and the boom in “unapproved” 88x31 pics demonstrates this