Meanwhile, the real program loads in the background, and a few seconds later will seamlessly replace the fake screenshot. They're just betting that your fingers won't be fast enough to hit the non-functioning buttons before the real ones take their place. It's kind of like a restaurant sending you out a photorealistic picture of a hamburger to make you think their kitchen is super fast, then quickly slipping the real burger under the picture while you're stuffing your napkin into your shirt collar.
A user named raygundan pointed this out in the comments at Reddit, and it sounded to us like a ridiculous urban legend, but it appears to be common knowledge among people familiar with the devices. Basically, the last time you used the app, your device saved a screenshot of it, then uses it to build the loading animation for the next time you launch it. It looks cool, you were none the wiser, it makes you feel like your expensive device is working more smoothly. And, the next time you use your iPhone, you'll completely forget that we told you this. You'll be blissfully enjoying their false reality, like a very small, sad version of the Matrix.
We guess you can file this under the category of Gadgets That Lie to You Every Day.