Well imagine they had to do a go-around on that landing. Go-arounds are extremely normal and might be done for a million reasons; your speed is wrong, your descent rate is wrong, your positioning is wrong, there's bad wind, there's an issue on the ground, etc etc etc. Six minutes of fuel is really not enough to be sure that you can do a go-around. So now, if ANY of those very normal everyday issues occurs, the pilot has to choose between two very bad options: doing a go-around with almost no fuel, or attempting a landing despite the issue. That's just way too close for comfort.
Aviation operates on a Swiss cheese model; the idea is that you want many many layers of safety (slices of cheese). Inevitably, every layer will have some holes, but with enough layers, you should still be safe; there won't be a hole that goes all the way through. In this case, they basically got down to their very last slice of cheese; it was just luck that the last layer held.
I think he would attempting a landing despite the issue in most cases because running out of fuel during go-around would be worse.