Does that mean I don't require a fuse in the circuit?
Good question.
If you short the power supply it will shut down, quite possibly before any fuse can blow. The danger is 40A into a partial short could easily start a fire. I think I'd go with the fuses; 5A to individual sections LEDs. A fuse won't do any harm and it might do some good.
You could short the furthest point of the tape from the PSU, then measure the resistance of the short at the PSU, with the wires disconnected from the PSU. If the resistance is more than:
5V / 40A = 0.125 Ohms, then you are at risk because the PSU could easily supply the 40A into a short at the end of the tape, the tape would go up in smoke and possibly your house with it.