Consensus seems to be that the photo is actually real, just not so out of place. From the Wikipedia page "Time travel urban legends" [1]:
> Further research suggests that the modern appearance of the man may not have been so modern. The style of sunglasses first appeared in the 1920s. On first glance the man is taken by many to be wearing a modern printed T-shirt, but on closer inspection it seems to be a sweater with a sewn-on emblem, the kind of clothing often worn by sports teams of the period.
Not sure how one can confirm the photo is actually real, it's so easy to fabricate picture nowadays and to add noise to make it seem like it belongs to the original. It's be interesting to actually have an in-depth article on the methods to detect fake pictures, I have seen a couple on HN but they only focused on a few examples.