The white wire w/ a black trace (10 ga.) from the alternator goes directly to the battery - no fuse or fusible link in the OEM wiring harness. You can run a parallel wire from the alternator directly to the battery but may want to consider adding a "Mega Fuse" (200 amp) to protect the battery. This is just a precaution because of the high amp output of the Mean Green. Also, many folks that run MG's bump the size of the wire from the MG to the battery to at least 2 ga. again to handle the additional amps from the MG. If the battery was drained and you tried to pump almost 200 amps through a 10 ga wire that's 20 years old you would probably melt something.
It sounds as if your troubles are running a little bit deeper than you think. The fusible links protect the wiring harness outside of the battery charge circuit. Did you use the wiring interface that Mean Green provides for plugging into the OEM wiring harness and the MG? If not this could be the issue. That little harness corrects the taps on the alternator to match the OEM wiring harness. Also make sure that your engine/body ground is sound.