1. The picture is most likely from the early/mid silent era, since the guy is wearing makeup which was common during that time in order to be seen better on film. Oliver Hardy did do early silent movies, but he wasn't as fat as the guy pictured during that time period.
2. Just because Stan Laurel is pictured two space over doesn't mean it's Oliver Hardy. If it was, I'm sure they could have gotten a much better picture (why not use the one they got Laurel's picture from - picured below). And, if you consider my first argument, Laurel and Hardy weren't an offical team until about 1928, right at the end of the silent era. Heavy makeup wasn't as common then, due to improvements in cameras and lighting.
3. Oliver Hardy never wore a yellow Derby. He's worn yellow Kangals, and other types of hats, but only black as far as Derbys go. Fatty Arbuckle did wear a light colored Derby, however.
I played around with the picture, comparing and contrasting images, and even trying to make it look more like Oliver Hardy by coloring the Derby black, removing the makeup, and adding a moustache... but now I'm even more confused. (BTW, the sites that claim it's Hardy, source Wikipedia - but Wikipedia uses those same sites that source it, as it's source of info... And if you change any of that information, so as to try to correct or highlight any possible inaccuracies, a mod will change it back so their little cycle of misinformation can continue.)