Of course you can be campy in Melee, it's a powerful tactic in Melee. Falco can run around and shl and if he's smart, he won't get punished for it. The opponent is forced to approach, just like we're seeing it in Brawl.
Marth can camp. Just hang around the ledge and space fairs and gimp your opponent when he approaches. Obviously this only works against certain characters, but against those that it does not, you have a different type of camping at your disposal. You can camp in their face. Just dash dance close to them. If they do a move, dash out of their range and pivot fsmash. If they try to shoot a projectile, run up and grab them. Until that happens, keep dash dancing and camping fairs in their face. They'll be scared to use projectiles, but they'll also be scared to attack. Which means they too will do something safe like dash dancing and moving around so they don't become predictable.
All of the top tiers excelled at camping in Melee. And here's another shock: camping is an art. Do you know what seperates Forward's lasers from some random scrubs'? It sure isn't the speed at which they fire them. It's how they're placed, how they're spaced, when to use what lasers, when to openly retreat and when to feign an approach. It's intricacy squared. The same thing applies to nearly every character. The truth is, camping isn't easy. Camping is not some method that scrubs pick up so they stand a chance at beating better players. It's another way to play, another option that you can pull out whenever you want it.
The reason people don't like camping in Brawl is because of the little punishment that you get from it. If you mess up camping in Melee you're dead, as Spam so kindly explained in a comment to that Pokefloats video. In Brawl, you just get hit once and go straight back to camping.
Thankfully, there are exceptions to this in Brawl. Let's take Marth, my main. He completely shuts down shields, thanks to the deadly risk of a broken shield at the hands of the shieldbreaker. If you hit someone's shield, all it takes is one more jab and the shield is gone, meaning the opponent is dead. So, once you hit peoples' shields a couple of times, they're going to be scared. If they use the shield, their most powerful option, they're at a great risk. Suddenly, the shield isn't so safe anymore! Since the shield is an extremely important part of camping, all of a sudden, your opponent's camping game is greatly weakened, and he may even consider stopping outright camping.
This is the only reason I even play Brawl anymore.