Yes, you're reading properly: Mewtwo CAN own in Super Smash Bros: Melee. In fact, there's a combo video of a pro named Taj, who is arguably the best Mewtwo player in the nation. His video can be found in the video section of the Super-Smash-Bros-Melee group.

Its not so much that Mewtwo can't be good (the video disproves that) its that its hard to be good with Mewtwo. Look at Sheik, its very easy to beat people with Sheik because of how easy to use Sheik is, can't say the same about Mewtwo.

It's the same as how I'm awesome with Pichu, but suck with Marth.