I think that is probably not correct.
From what I've heard, the stock turbo is just too small, maybe 200 at the wheels is possible but to get more a turbo upgrade is likely required.
Once you take that step things get interesting. Any way you slice it, a turbo upgrade isn't going to be cheap and there isn't much out there that is size appropriate. Too big means you lose that quick spool at 2,000 rpm so you want the smallest turbo that can support your HP goal and with all the tricks to decrease spool time.
That points me to the Borg Warner EFR 6258, its about the same size as other options but it has ceramic ball bearings, water cooling, a Titanium Aluminide impeller for much lower inertia than Inconel or other super alloys. That's a turbo that can support close to 400hp. I think on the 1.6 it should easily support 270+ whp if the high pressure fuel pump can keep up and its going to spool about as well as any other upgrade option.
I figure its about a $5,000 upgrade if you can do a lot of the fab work (turbo, header, down pipe, exhaust, cold side plumbing, FMIC upgrade, Accessport with Access Tuner Race, probably a custom cam to help the high pressure fuel pump, etc.