Remember kids... always wear a helmet. (The almighty bikeradar helmet thread)

Hoping that a driver is more careful around you because they have spotted you are wearing a helmet (consciously or subconsciously) is probably not a good thing to bring into any objective safety discussion.

You have it the wrong way round; they go closer to the helmeted rider. And it's exactly the kind of thing we need to bring to an objective discussion. To exclude a known factor which seems to reduce safety margins for helmeted riders suggests an agenda

I would also think that any sort of data to suggest helmets wearers were on average given a wider birth is questionable as the drivers giving the wider birth are different drivers, i.e the same driver may give the same birth to the same rider regardless of helmet status.

It's pretty obvious that you'd get a wider birth if wearing a helmet, since the head is the widest part of the infant and anything which increases it will require more dilation.

Jokes aside, this is why we ignore anecdote and study populations; if you measure the passing distance enough times, you get a statistically significant view of whether some factors relating to the cyclist influence the behaviour of a population of drivers. Of course, some drivers pass wide and slow regardless of who is riding, and some seem determined to clip your elbow with their wing mirror whatever you're wearing, but the distribution curve does seem to shift slightly according to cues which inform the driver about the perceived expertise of the cyclist. If you've ever been circumspect when passing a Boris Bike, you've experienced the effect.