This topic grabbed my attention, though not because I get headaches from draft beer. I had a measly four bottles of my homebrew Saturday night - two each of two different beers - and had a hellatious headache all morning on Sunday. Now I can easily drink a bottle of wine or mead and feel great the next morning so this headache had me puzzled.
I looked online and found a reply to a similar question. The reply was given by Ed Westemeier, "Award-winning beer writer, columnist, and brewing consultant, as well as Grand Master Beer Judge."
There is a chemical that causes headaches for about 1 person in every 15. It's a natural byproduct of certain strains of brewer's yeast, not something that is added to the beer. Switching to the products of a different brewery that uses a different strain of yeast for their fermentation will often clear up the problem.
Even though the breweries that have this difficulty are aware of it, they don't change their yeast because doing so would also change the flavor of their beer.
I should mention that every strain of brewer's yeast produces this chemical byproduct, but only a few of them have it at such a high level that it affects people. The Anheuser-Busch breweries just happen to be one of the highest.