Let me explain why what he did was theoretically dangerous and why the rules are very specific.
While compassion is good and all and jumping right on the he saved a man train is fine, think about the full situation of why they have a rule like "Don't go outside your zone". These Lifeguards are assigned certain areas to watch. If this lifeguard leaves his area un-watched in order to do something in someone elses area, who saves someone if they start drowning in his jurisdiction?
Yes, this is an almost ridiculously improbable scenario, but the rule is there for that possibility. Outright firing the guy was a bit of a steep reaction (they did later offer him his job back), but the rule isn't there for no reason. Ask some Firemen sometime if they like heroes, or the people who do their job by the book.
In this case, everything worked out well and there were no complications and so I think that it would have been more appropriate to reiterate to the lifeguard why his duty reads the way it does and reprimand the lifeguard whose duty it was originally to save the man in question.