Even if you choose people at random and phone them up, you still only poll people who have a phone, and people who pick up the phone, and people who are willing to answer your question.

The question you have to ask yourself is if any of those things are likely to be correlated with political opinion. If democrats and republicans are equally likely to have a phone, pick up the phone and answer your question, then it can be considered a random sample (at least if you pay attention to where people live, what they do for a living, and a whole load of other things which are correlated with political opinions.

In this case, there is no reason (that I can think of) for potential strength in the power among people who don't know if the can channel to be correlated with desire to become Aes Sedai. Which means that using people who walk into the camp, asking to be tested, a perfectly acceptable way of obtaining a random sample for the purposes of measuring strength in the one power.