Photgraphs of distant galaxies show them as they were when they were much younger than they are today

True.
The reason why photographs capture images of distant galaxies much younger then they are at the moment the photograph was taken is because a picture that is taken can see what you see. What I mean is that you can see things because you're receiving the light produced by distant objects and by the time you can see distant objects the light has already been traveling. An Example of this is our sun when we look up and see our sun we're seeing about 8 minutes into the past because of the time it takes for light to travel from the sun to our planet.
Hope this helped.