You do realize that there are two parts to the tire/wheel combination that result in the total height of the package? Yes, it's true that decreasing the wheel size could increase the gap between tire and wheel well if the amount of tire outside the rim were to remain the same. But the whole point of what we used to call +1 or +2 or +3 sizing is to maintain the same overall diameter of the wheel/tire combination when you vary the diameter of the wheel. You do this by varying the aspect ratio of the tire, which is the percent of the section width that the sidewall height measures. The number after the slash in a tire size represents the aspect ratio. The standard Fiesta tire is 205/40-R17. It has a 40 aspect ratio. If you drop the wheel size an inch by going to a 16" wheel, or two inches (-1 or -2 sizing), you can maintain the same overall diameter by increasing the aspect ratio of the tire to 45, 50, 55, or 60, depending on the section width you choose.
In the photo you supplied, you can clearly see that there's a lot more sidewall between the edge of the rim and the surface of the tread than on the standard 17" wheel. This means the tire has a taller aspect ratio than the original. The standard Fiesta tire has a diameter of 23.5". Dropping to a 15" wheel, you can get close to the same diameter by using a 185/60R15 (23.7"), 195/55R15 (23.4"), 205/50R15 (23.1"), 205/55R15 (23.9"), or 225/50R15 (23.9"). The car in the picture is lowered as well, probably by about an inch or maybe inch and a half.
If you wanted to use 16" wheels, you could use 205/45R16 (23.3"), 215/45R16 (23.6"), or 195/50R16 (23.7").
There are tire size calculators online that allow you to see these numbers. The one I used to post this is at
tiresize.com/calculator