Depending on which transmission has been fitted to wrcsti's (Dad's) car, it will either have a theoretical topspeed of:
158 mph (254 km/h) (6th gear 0.842), or
176 mph (283 km/h) (6th gear 0.756). Most commonly fitted US-spec transmission.
That is on the rev limiter in 6th. Don't forget though that maximum power is 1000 revs down the range; once beyond 6000 the car will not pick up speed very quickly, if at all.
So the effective top speed of a 2005 US-spec STi is:
151 mph (6th gear 0.756).
So, I guess what I would say to wrcsti is that, it is theoretically possible to do what you said you did, but I find it unlikely that the car would get anywhere near the limiter in 6th.
Another factor that comes into play is the inaccuracy of a car's speedo. Having played with Subarus a bit, even though the speedo may read 160 mph, your actual speed is likely to be around 145 mph.