Width is OK as long as you get the right offset. With the wrong offset - you could get even the OEM tire to rub on a different wheel.
On the 2003+ Corollas - I was told that you could run an offset from 35mm-45mm. Most 16" wheels are anywhere from 38mm-42mm, depending on the vendor. On mine - 16x7 wheel rubbed with a 38mm offset - but cleared with a 40mm offset. But the 40mm offset wheel came very close to touching the struts. I believe that the 9th gen have a bit more room to work with.
Of course this is complicated if you have a dropped suspension. Most people ended up getting the wheels they wanted and if they rubbed - rolled the fender lip to make them fit.