The problem was that most scientists would consider that neutrinos being able to travel faster than light so unlikely that even if no source of experimental error could be found, it would still be almost certain that it was the cause.
So if it was needful to publish something in order to establish priority, it should still have been presented in a very cautious way, so as not to cause embarassment by implying that any of the scientists involved ever for a moment seriously believed that any neutrinos were actually going faster than light, despite all the measures they took to eliminate known sources of possible error.
The eventual discovery of the loose connection was not the blow that destroyed the credibility of those involved. That, instead, helped to restore some of the credibility lost in the initial announcement of the apparent discovery.
Despite open-mindedness being an essential virtue in science, this incident has led to the suspicion that some of the scientists working at CERN are a little too open-minded.