The 2007-08 Upper Deck First Edition basketball set has a rookie insert set called "2007 NBA Rookie Draft Notices."
A picture of the player is on the left of the card. On the right appear the words "ORDER TO REPORT." Below that reads "To: (player's name)." In a small box labeled "SELECTIVE SERVICE INFO.," you can see the date of birth, hometown, position, and team of the player. Below is an image of a red stamped seal. The seal is a circle with an eagle in it; the circle includes the words "SERVICE REQUESTED" and a banner in the seal reads "DRAFT NOTICES."
Let's accept that the word "draft" for conscription into military service and the word "draft" for selection to a professional sports team has the same root. The Oxford English Dictionary (institution subscription required) includes the following noun and verb definitions with usage as early as the 18th century: "The drawing off, detachment, or selection of a party from a larger body for some special (spec. military) duty or purpose; spec. (esp. in U.S.), selective conscription" and "To draw off or out and remove (a party of persons, animals, or things) from a larger body for some special duty or purpose. Chiefly in Mil. use, and in Stock-farming: see quots. Also (chiefly U.S.), to conscript." The word has the meaning of selection for special service, but was usually associated with military service well before pro sports leagues held "drafts" (the OED doesn't even include reference to a sports draft), so I suspect sports leagues borrowed the term from the military usage.
Even if pro sports borrowed the word draft from the military usage, isn't it a little extreme for Upper Deck to make such a clear analogy on a card? "Draft Notices" sent by the "Selective Service" System inform men that they are being required to report for military duty, where they must sacrifice whatever plans they had for their lives, get training in how to kill people, and then possibly risk their lives in warfare. Is it responsible for Upper Deck to draw such a clear parallel between conscripts and basketball players, for whom a draft notice means playing professional basketball for millions of dollars?