First off, I'm not convinced that this rumor is anything more than just that - an attention-seeking rumor. I've been hearing rumors about an 'iPhone nano' for some time now, and after the iPad, a device which is four times as big as the iPhone, there's a certain poetry to the idea of a device half the size of the iPhone. But we need more than poetry to make this rumor work.
But could an 'iPhone nano' work? Well, the place to start with a project like this would be to shrink the screen. Given that Apple doubled the screen resolution of the iPhone 4 compared to the 3GS (up to 960x640 from 480x320), you could, theoretically, make a screen half the size and have apps run fine on it (apps that work on the iPhone 4 and 3GS at any rate). Sure, it wouldn't be a retina display (I'm reminded of Homer Simpson's "Picture so blurry, might as well rub dirt in my eyes" pout), but it's still a display.
Problem solved then, right? Wrong.
I don't know if you've looked inside an iPhone 4 (or alternatively taken a look at a teardown), but there's a lot of stuff inside them. A LOT. Even if you halved the size of the battery (something that's possible to do, but which has an adverse effect on how long the device can last between recharges), it might not be possible to halve the footprint of the remainder of the electronics without some radical re-engineering. Even then it might not be possible to get it all down that small. After all, it still has to be an iPhone and do everything that the iPhone currently does.
Let's assume that this miniaturization is possible. Job done, right?
Not so fast! What about the OS? Fist thing that comes to mind is the on-screen keyboard that Apple uses. It's already pretty small, so the idea of using it on a screen half the size of the current iPhone screen doesn't bare thinking about. I'd hope that Apple would provide us all with out own Apple-branded pinhead for driving the UI.
The rumor that Apple Insider has does mention 'voice navigation,' but the idea of doing everything via voice is far-fetched. No matter what size the screen, the UI would need to be usable. Voice is currently a long way off being usable on the iPhone.
The more I think about the 'iPhone nano' the more I feel that this is just one of those rumors that sounds good, but when you stop and think about it the only way that this would work is if the 'iPhone' in question represented a radical departure from what we currently think of an an iPhone. There's talk of it having only a small amount of internal memory and using the cloud for storage, which not only means a redesigned iPhone, but a redesigned way of using the iPhone.
That could be an interesting experiment.
[UPDATE: 'iPhone nano' starting to sound a loke like the iPod nano now. I'm more confident that this rumor is just nonesense now.]