It is important to stay tight, but not too tight. It is important to stay tight enough that you hold the correct positions throughout the lift to ensure the bar gets to the right spot. On the flip side, you don't want to stay too tight. This isn't Powerlifting so you don't need to breathe and squeeze to the point where you're eyeballs look like they're going to pop out. The reason for this is because Weightlifting is a change of direction sport and about generating velocity on the barbell.
What this means is that in order to accelerate the bar appropriately we need a release in tension. If we don't get this release in tension, then the bar isn't going to change speeds and we aren't going to be able to change directions either. Just like a pitcher has to know how to release tension at the perfect moment so the ball zips out of his hand, a Weightlifter needs to know how to release tension so he or she can accelerate the bar and get under at the same moment. It is that feeling of weightlessness, and you can't get it if you are too "tight."
This is why "stay tight' isn't the best cue in Olympic lifting and we should be more focused on cueing someone to get in the right positions at the right time.