You are talking to someone who does this for a living.
I will have to disagree with this assertion, but to go off topic, of course you can't have a perfectly random selection process, but by policy, you can have a degree of randomness. For example, if you wanted 100% screening, you would check everyone. If you wanted 50% screening, you could implement that by flipping a coin on every one that showed up. You could also leverage presumed "random arrival rate" by taking 50 out of every 100, or 500 out of every 1000. You are leveraging the fact that every arrival instance is markovian in nature and thus independent from the preceding 1,2, 3, 50, or 1000 arrivals. And also, while you are sampling a million people, it doesn't matter if you are sampling every other one or the first 500K out of a million. Again, this is presuming that arriving population is random.
If you determined that the arrival process is Gaussian and wanted 1 sigma representation (a single standard deviation), you would sample 66.7%. Or - you could just wag it and by policy say that you want approximately a third of the arriving population. It is still random if you applied a uniform random number generator or picked approximately every third person. Now all that said, arrival rates might not be random because in culture, the kids run ahead of the adults and the gentlemen let the women go first, and there are average family sizes so you can get some aliasing affect if you sampled every N. And I agree that every Nth checking isn't a great idea because a diabolical terrorist can count people, but if he is going to go through great lengths, it is easier to take a heavy weapon to a shopping mall.
So getting back on point, if I am a family of 5 and it was truly random, I would expect that if I showed up every day for say a hundred days, I would be singled out 20 times.
Based on a very limited sample set of a 4 day park hopper, it sure did not feel random to this person.
Also, Disney is the one claiming that it is random - and it well might be, but we will have to disagree on the level of selection that they use to pick out people. I also iterate that I never said that there is anything wrong with it.
Finally, I said in original post that just because you are harmless and selected or with a harmless person that was not selected, this does not preclude Disney from having a policy of applying criteria when they select people to go through.