I run 225/40/18's on a 18x8 ET45 wheel on my GTI... its perfect fitment and no stretch, tire doesn't "hang" over rim either.. its nice and flush like.. Its perfect.

Does a tire stretch if the wheel is in fact more wide? An 8.25 wheel is 210 mm. How much wiggle room is needed to mount with no stretch? The pictures of the brz with the same wheel tire specs as I could have doesn't look bad at all. I just want it to be safe.

Like i said it varies from tire to tire. You need to look up section width vs overall width too. There are several ways these things are measured.

Section width of the wheel or the tire?

Both. Some manufacturers interchange overall width and section width... it can get confusing. Like i said the actual contact width of the tread on a 275 nitto 555r is an inch narrower than it should be. Goodyears tend to run big on the other end of the spectrum.