Why would this happen?

Hey guys, I recently pulled out the carpet and insulation and there was rust, but only on the passenger side. The drivers side was in nice shape.

The cowl doesn't leak, its sealed. But... I do remember that when I got the car the heater core was busted. It was pretty bad and I could tell that they were original heater hoses so I doubt he ever replaced the heater core. When my parents bought the car all the owner said was that the heater didn't work well. So...who knows how long the heater core was leaking...

Would that be a contributor to the rusting? another cause might be is the fact that the seat bolts don't have plugs and grommets underneath.
 
The heater core was most likely the culprit, or at least a major contributor. Heater cores go bad a lot because people don't flush their cooling system enough. It looks like yours did just that. They tend to leak slowly at first so most people don't really notice it or they just ignore it and will "fix it later". Touble is the rust starts fast. I've had several 66 Mustangs and they all had the usual leaks; winshield, heater core, cowl vent, but one had a leak that took me a year to figure out. I took everything apart, put cowl vent caps and resealed the winshield several times but still it leaked. Turns out a hole had rusted through the firewall in the fenderwell and water would seep in through it.
 
I don't have an A/c, I replaced the heater core but i didn't replace the hoses last time, I will this time. I pulled it out to put in new sound dampening plus the painter didn't cover the cowl while sanding and now the vents are full of dust and what not. So i'm gonna clean the heater box out .