Can a DC power source, such as batteries, cause over-voltage or current spikes
Discard that website. The infomation they give is ill-advised to wrong.

You cannot power the Raspberry Pi through the GPIO pins. You can power it through the power pins of the 40-pin header. The only difference between doing that and using the Micro-USB power input is a fuse in the +5V line. As the +5V line is routed directly to the other USB ports, you can burn out the copper traces on the Raspberry Pi board if you use a powerful power supply at the 40-pin header and produce a short circuit on the USB ports.

The other traces on the board are protected by the fact they are behind voltage regulators with built-in current limiting.

"Burning out" GPIO pins happens when clueless people connect too high loads to them, or connecting them with +5V or even higher, instead of at maximum +3.3V. This isn't related to the +5V power supply.