I'm willing to bet my left nut that it is not a photoshopped picture. You will have no difficulty in fitting 19" rims to the Mazda 3 as long as you don't try to go too wide and your offset is correct. If I remember correctly, those wheels have +45 offset and you can tell in the front that the tires are sticking out of the fenders just a little bit. I believe as long as you get wheels no wider than 7.5in with an offset of +48, you should be ok.
But I'll say again, the large wheelgap is a result of the suspension being too high and not the wheels you pick for your car because the diameter of the tire should be the same as or close to stock.
Finally, if you do a search for the Kenstyle Mazda 3, you will see it's got 19" rims also (or was it 20"?).... The reason you don't have the wheelgap on that car is because it is lowered.