I think that your friend doesn't understand the purpose of a fuse. Fuses
do two things: 1) they protect the wire from overcurrent that could melt the insulation
and start a fire and 2) they protect the appliance (motors, etc) that they serve.
Since a PV panel can't be harmed by current
that it generates and most have blocking diodes, the only purpose of a fuse is to protect the wire. The fuse needs to be sized to match the ampacity of the smallest guage wire in the circuit. The overcurrent is comming from the battery
that it feeds not the panels.
Your 4x130 panels can generate about 30 amps of current
combined in parallel. So I would wire each panel together with 12 guage and then wire to the controller with 8 guage. 12 guage is good for 45 amps so a 40 amp fuse near the battery
will protect it.
If your controller will accept a high voltage input- 40 volts or double the open circuit voltage of your panels, then you can save a bit on wiring
cost by wiring the panels in series/parallel so that double the single
panel voltage is supplied to the controller. Then your current is cut in half and you can wire the panels with 14 guage and make the home run 10 guage.
Increase the guage of the home run if it is longer than about 30 ft round trip to minimize voltage drop and power