This is patently untrue of a Fox Mustang. The 80 amp alternator and undersized wiring in Fox Mustangs was a hazard from the start. Now, the newest Fox is 24 years old.
No Fox Mustang is complete without a 100 amp or higher alternator upgrade and associated 4 gauge wiring upgrade and fuse.
If you have ever seen:
lights dim at night with the turn signal on or changes in air-conditioning controls
had slow cranking after short runs
or seem to eat up batteries in short order
then it's likely you need moah powah
Our alts are junk and barely adequate. A 3G alt upgrade is easy and relatively inexpensive. It will also charge the battery at idle (our stock alts will not).
Alternators out of the way and as Karthief mentioned, the wiring and harness going into our 2G alts is inadequate and will not bear the full load of the alternator for very long. Even if sticking with the stock 2G alt, an additional supply wire from the alternator to the positive side of the starter solenoid (fused of course) is always a good idea and will prevent the situation you describe in your initial post.