Melted ground wire
It SHOULD unless the ONLY other ground wire is somehow not making a good connection.
Doesn't matter in this case.
Short was occuring with key off.
If the starter was running, and the engine ground cable was poor, then yes, the body grounds would try to carry the current.
In that case I'd agree the problem was a poor engine ground.
But in this case its big current with the engine running, and then even with the engine off.
That 10 gage ground is capable of handling pretty much every device running at the same time. Lights, heater, wipers, radio, horn, brake lights all at the same time is roughly 30 amps. All those electrons will flow back to the battery at the same time though the same wire. Or if the engine is running, then onto the engine ground to return to the alternator. Either way a 10 gage wire should easily handle that.
Sure there also should be a engine to firewall ground, so two paths, but that's not the heart of the problem here.