What difference does it make if I substitute low-fat milk for water in bread recipes? I'd like to know whether is it possible to always substitute milk with water (or the other way around) in bread recipes and what difference does it make? For example, in the following recipe that I found here:

Honey-Oat Pain de Mie


255g lukewarm water
361g AP Flour
85g old-fashioned rolled oats (not quick oats)
1 1/2 teaspoons salt
64g honey
57g melted butter
2 1/4 teaspoons instant yeast
Off the top of my head, the added sugar from the milk may cause the yeast to over-leaven the bread.  The opposite is true when substituting water for milk, you may need to add sugar.

Edit: According to this site, Glutathione in the milk must be destroyed by heating it first, otherwise it tends to inhibit yeast.  Also, allegedly lactose doesn't contribute as much to the yeast activity as I thought, as it doesn't break down as fast as raw sugars.

Other sources seem to corroborate the fact that the bread is softer with milk.

Some others may be able to add more insight ...