Barrera's speed and stamina may be suspect, just because of age and a lot of tough fights, but I don't think his chin is suspect.
As you said, he spent 36 rounds in the ring with Morales and never went down (although he did go down from a body punch in their second fight, it was ruled a slip but I thought it was a knockdown).

He got battered for 11 rounds by Pacquiao but was on his feet when the fight was stopped. Could Marquez hurt Barrera? Sure. But Barrera's chin isn't suspect.