I agree to an extent with Draug and Celtic. If one can take a step back from the situation and pretend that there's a list of things that are reasons you may avoid military service, and that homosexuality is on that list, then of course you would need to prove it just as you would need to prove a physical impairment or psychological impairment. Since we do not have a litmus test for homosexuality that a doctor can sign off on like (s)he can one of the two other mentionable, standard reasons to avoid service, then there does need to be some proof for the orientation.
However, I also agree that such graphic pictures are not necessarily the best way to measure whether one is genuine or not, primarily because the article describes homosexuality as being a shameful status in Turkish culture and that these pictures are often used to shame individuals to their relatives, friends, and other loved ones, and strangers. Curiously, then, this shame is not coupled with laws against the orientation.