jmlease1 already echoed my reasoning, but just to elaborate, for me it was a principle of greatest-regret, and/or a greedy heuristic. Of course the "value" of each player is left up to individual posters, but the prices are set by your article. For each of the 11 positions, decide a numerical amount of "regret" from having to go with the best choice versus having to settle for the value of someone else. Among these 11, start by picking the positions you would regret the most, lather, rinse, repeat. For me, those were CF, 1B and C. I used Wins Above Average for their Twins career; some other metric for value, where the differences at the top would not be so large, say a numerical value for how much you love each player, would result in very different choices. Anyway, to answer the specific question about relievers, the WAA for Joe Nathan was not enough higher than the others to exceed the regret for losing, say, Puckett, and the regret going further down the reliever list became even smaller. Davis would have been the logical choice, but as I said before, I had some fun with it.
This greedy heuristic was key to success in one of the first analytics projects in my career, a military logistics problem, and so naturally I remember it well, and use it any chance I get. How a baseball all-star team relates to moving military units is probably best left for another time...