How can I record video of the iPhone screen without jailbreaking the phone?
Don't overlook the power of running things in the iOS simulator. Xcode is free for Lion users. This is a very limited solution since you aren't really on the iPhone and you can't run app store apps, since its running computer versions of the apps, not the ones you download from iTunes.

Being a paid developer allows some extra flexibility in capturing the screen while tethered, but this might be an alternate.

Until this becomes a feature, you'll be stuck with this and the other options you have ruled out - a real camera or jail breaking to modify the code and get a dump of the screen.