You're absolutely right. But what is "close?" An alligator swimming right alongside the boat? Sure, that's definitely too close. But what about an alligator on the riverbank, 100 yards away? Is that still too close? How about half a mile downstream? Again, I've never lived near gators, so I don't have an intuition on what is and is not a dangerous situation.
Additionally, I feel like you're forgetting that oft-repeated (and generally true!) maxim: "They're more afraid of you than you are of them."
Maybe the father in the story was being outrageously irresponsible. My gut tells me (and the story seems to intimate) that he knew what he was doing. That is, he probably intuited that the situation was low-risk.
To use a different dangerous animal, people have been killed by grizzly bears, yet tens of hundreds of thousands of folks annually camp out in the backcountry. Are they being irresponsible, just because their is a risk involved?