“…can you put 17” rims on a car that comes with 16" rims?"
Most of the time. It appears according to what Ed posted that in your case you can. I suspect that is want they were trying to say.
Personally I would not do it. Those large rims with thin tyres tend to be subject to damage from potholes and alike and I doubt if the whole thing would be cost effective. If those are not thin tyres then the overall size of the tyres are going to change throwing off the speedometer odometer and gear ratios.