A couple of things you're missing: If the STi was in 3rd gear, and you were at a 60 MPH rolling start, the STi would be at about 4000 RPM, right smack dab in the middle of its tourque peak with the turbo fully spooled and ready to go. Contrary to popular belief, there is noticeable turbo lag on the STi.
If the two of you are shifting into 4th at the same time, then the STi driver wasn't full throttle. The gearing difference between the two is huge, and the 3rd-4th shift is at about 75 MPH in the STi, which is lower than most cars out there.
At 115, the STi still pulls strong in 5th (the fastest I've had mine), I don't know what the runs out in 3rd gear was reference to.
Polygon summarizes what an intercooler does quite well.
I consider the STi to be an extremely good value for the money. Aside from the EVO, what other new cars are out there that you can get that have 250 HP and a factory warranty for under $40k US?
Oh yes, and it's snowing here today too. I feel sorry for anyone with a RWD car in conditions like this.
__________________
2004 Subaru Impreza WRX STI (daily driver)

1999 Mazda Miata (track car, slow, but finished the SCCA Runoffs)
1987 Porsche 944 (being rebuilt)