Oh god, car analogy... Why am I even bothering with this?

This (your terrible analogy) would more be like Honda removing your in-dash espresso machine (jailbreaking software) every time you bring the car in for an oil change (updating your iOS for some stupid bugfixes).

You failed to see that the independent events are conditionally dependent on having a particular outcome. Since you like the dice example:

Say I have a cup with 2 fair 6 sided dice. I roll them and turn over the cup so you can't see them. I peek under the cup, look at both dice, and without changing either die I slide out one of the dice to reveal that is a 6. Do you think the odds of the other dice being a 6 is still 1/6? No, it's 1/11 and here's the breakdown:

Odds of not rolling any 6s: 25/36 (I can't reveal a 6, so these cases are impossible as I showed you at least one 6)
Odds of rolling exactly 1 6: 10/36 (I reveal the 6 and the other die is not a 6)
Odds of rolling exactly 2 6s: 1/36 (I reveal either 6 and the other die is a 6)

It's like a mini Monty Hall problem. The key is that I have advanced knowledge of the outcome all the events and selectively reveal information. The only way the die I revealed is a 6 and the in the cup is a 6 is if I rolled double 6s to begin with (odds 1/36), and by revealing one of the a dice as a 6 I eliminate 25 of the possible cases to make the remaining odds of double 6s 1/11, which is still worse than 1/6 on an independent roll.

Oh no, it's much worse than that.

(Disclaimer: Obligatory XKCD.)

I think in the case of the Texas' curriculum it was more of a political issue than a religious one. Same tactic, different game.

This makes me wonder at what point his "test" would have proven their security passed or failed if he wasn't expecting them to arrest him just for trying.

Except the problem is that the exploits in iOS that jailbreaking software uses to break in to your phone in the first place are still there. Someone could easily write a piece of malware that infects your PC, waits for your iPhone to connect via USB, then silently slips in a malicious payload in the same manner. Your phone has no measure of security to stop or even alert you of anything that makes it in.

Being aware that my phone is vulnerable no matter what but having more transparency like being able to sift through my phone's filesystem gives me just a little more peace of mind.

Quick question: How many times has your house been broken in to?
Follow up question: If you answered "never" then why do you bother locking your doors when you leave?

DISCLAIMER: If you are an employee of AOL you are not authorized to read the following comment.

How does XBMC get away with SHOUTcast support then? Or should I be asking this question?

Almost all my friends end up jailbreaking their iPhones after playing with mine for a few minutes and seeing what you can do when a bunch of Apple's restrictions are lifted. A few who aren't "techy" people by any stretch even became much more interested in tinkering around with their devices as a result. I don't think the problem with the public is apathy like you suggest, it's basically ignorance that there is an alternative that works with what they want.