YOU sir are wrong. Aperture does not affect noise. The actual sensor size is what affects noise in addition to the ISO (which is a term referring to a film's sensitivity to light and now translated to digital).
A smaller aperture (larger number) does not mean more noise. It means that the actual hole letting light in, is smaller. Obviously with phones not controlling shutter speed (which a phone doesn't have an actual shutter) or ISO, a larger aperture is desirable. But I do reiterate, smaller aperture does not influence the "noise" in a photograph.
I'm sorry to correct you but I'm a professional photographer, and I know what I'm talking about. Although the iPhone may not be a professional camera, it does have a shutter, albeit an electronic one, otherwise it would be unable to record an image. Every image has a well controlled exposure time and ISO that is set by the phone based on the calculated correct exposure. To prove this, take an image in low light, and shake the phone. It will be blurry due to the longer exposure. Do the same in bright daylight, the image will be less blurry, showing how much shorter the exposure time is. Also observe the increased noise in darker scenes, this is due to increased ISO. These are basics of photography, every camera does this, even the cheapest, smallest and crappiest ones.
If you still don't believe me, read the metadata from the image files your phone takes, or go to Flickr and read the metadata from other people's iPhone pictures. It will clearly say the exposure, ISO and aperture values, and the first two will all be different on different photos. The aperture is not variable on the iPhone, as it's the only thing that would have to be mechanical, so the phone has to make do with changing the ISO and the shutter speed. How else would it change the exposure to match the scene?
Indeed, a smaller aperture, in itself, means nothing for noise. But if you take a sensor paired with a smaller aperture, and then the same sensor with a larger aperture, then the one with the larger aperture will be able to achieve less noise, as it will have enough light to achieve a lower ISO, while the smaller aperture will force the camera to increase the ISO and/or the shutter speed, resulting in more noise eventually.
Noise depends on the sensor size and type, but also on the ISO. The higher the ISO, the more noise, when comparing identical sensors. The smaller the aperture, the less light, so the higher the ISO will have to be, increasing noise.
Sensor size allows for more light to be detected, making higher ISO settings less prone to noise. But higher ISO will always result in more noise in the same sensor.
So, if you take the iPhone's lens and give it a bigger aperture, the phone will be able to produce less noisy images, and/or faster shutter speeds. Chances are it will do both, as long shutter speeds are just as undesirable as noisy images.
Therefore:
Smaller Aperture = Less Light
Less Light = Compensation by increasing shutter speed and/or ISO
Increasing ISO = More Noise
Increasing shutter speed = More motion blur
So: Smaller Aperture = More Noise in many of your photos
Read this article for more info, especially the part about ISO:
http://www.cambridgeincolour.com/tutorials/camera-exposure.htm