I think anyone who is coached as a DE or in a position that is supposed to have outside containment is coached to be as deep as the ball at all times.
Ray, IIRC, is a WR by trade. This was not defense, it was special teams punt return. (I assume return was on, but I don't KNOW that) I also don't KNOW what his actual responsibility was, but I do know that generally speaking on PUNT RETURN, there's usually one guy, or 2 who have a responsibility to rush the punter. Their job is not to block the punt, but they can IF they can do so. Their primary job is to rush the punter and make sure the ball is kicked. They are usually aligned to the outside of the box as Ray was. If he was not assigned to rush the punter, he then most likely had responsibility to jam a particular man at the LOS, then trail him down field and attempt to regain a good blocking position. As always, he had to be aware of a fake punt, but at that point, when/if he reads fake he simply turns in to an athlete and does his best to make a play.
IF...IF somewhere, and somehow he was ever given a task to "contain" then it likely consisted of being told that as a mental note, and little time was spent coaching it.
In most modern defenses the DE's primary responsibility is a gap. There may be certain calls that change this. Usually it's C gap. They move with that gap laterally and spill runs to them to the outside to be cleaned up by a LB or S. or when they read pass they rush. If they read RUN AWAY they then become backside contain. If this were our defense, and a DE, then I'd say whoever it was lost their backside contain. This was punt return, and a WR not defense or a DE. Melvin Ray was probably given next to no coaching in defensive techniques and I'd wager he does few tackling drills.
As I conceded, I don't KNOW what his job was and don't know what the return team's call was. IF he was given a task to play run contain, then it was a bad personnel decision as Snags points out. I'm not going to blame a WR for being sucked in by a fake punt run and getting burned on the reverse if there wasn't even a "Punt Safe" call on.
If there was a punt safe call on then it was poorly played in many aspects including Ray not playing contain.