Amperage discrepancy between AWG size/property chart and amp user manual.

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Trying to work out power distribution for a build I'm planning. I have 3 amplifiers that all accept 4AWG 12v/GND and call for 30A, 60A, and 80A line fuses respectively. The AWG size and property chart says that the max safe current for 4AWG is 60A. Can anyone explain this discrepancy? The last thing I want to do is set my girlfriend's $30,000 car on fire.... My goal is to fuse each of the 3 amps at the distribution block, and then fuse the whole circuit near the battery, but due to these discrepancies I have no idea what the correct amperage would be for each fuse. I'll put the specifications for the whole build below in case it helps. Thanks in advance for your guidance.

 

- LOC/DSP: Audio Control LC7i Pro

- Amp 1: Crunch GP 2000.2 

- Sub: Stereo Integrity SQL 15

- Amp 2: Rockford Fosgate T600-4

- Front door: Earthquake SWS6.5x 

- Rear door: Kicker KS 6.5" Coax

- Amp 3: Rockford Fosgate P400X4

- Dash: Kicker KS 2.75"

- Pillars: Kicker KS .75" Silk Dome