For instance, this bit: "the general pattern is that more complex cameras take better pictures". That's certainly true. Think about the person behind the camera, though. If they own a dSLR, they're more likely to be good at composing photographs.
This, too: "a 28 year-old who used a flash is as attractive as a 35 year-old who didn't". Most people don't know how, or even when, to use a flash. Using a flash properly can and does lead to a better photograph, but it takes a lot of practice.
Therefore, if you want to have an attractive picture, have somebody that's good at taking pictures take it.