5 m, 5 V LED strip 20 A PS = Fire?
They state 60 LEDs/m @ 18 watt/meter, thats 3.3 W per LED?


0.3 W per LED, they're assuming the standard 60 mA per diode for RGB 5050 SMDs.


  By the looks of it if I wired in my 5 V, 20 A supply to both ends it would still set fire.


20 A is how much current the supply can provide, not how much it will actually give when hooked to the load.  Those tiny traces have a lot of resistance, so if you try to hook up 5 m, you will get a lot of voltage drop, many or even most of the LEDs won't turn on and the actual current load will be much lower.  Hence, no fire (and not much light).

To use that many LEDs you will probably have to wire a bunch of shorter strips in parallel, each using a current of a few amps.