If the engine stops because the pilot ran out of fuel the outcome really isn't any different than if it stopped because a bearing failed or the lubrication system failed or a crankshaft sheared. The end result is the same - no power, and you have to glide.
But few light plane fatalities are caused by an engine stoppage in a single engine aircraft. The vast majority of injury and fatality accidents occur to light aircraft with engines that are running fine and an airframe that (until the point of impact) was undamaged.
As an example: I picked April 2011 from the NTSB monthly list of aviation accidents (it's long enough ago that all the fatal accidents will have a probable cause listed, but recent enough to be relevant to today's aviation environment).
In April 2011 there were 20 fatal aviation accidents:
Out of these, the causes were:
2 caused by pilot incapacitation
1 caused during flight testing with one engine deliberately shut down
1 caused by the pilot selecting the wrong fuel tank then losing control of the aircraft
2 controlled flight into terrain in poor weather
2 caused by engine failure but the pilot lost control of the aircraft
6 caused by a straightforward loss of control of a perfectly good airplane
1 caused by a drunk pilot losing control during a night landing
1 caused by loss of control of a multiengine aircraft with partial power loss in one engine
1 hit the ground while performing low altitude aerobatics
3 flight in instrument meteorological conditions and subsequent loss of control
Only 4 of these 20 had anything to do with loss of power (I'm not counting the one where they deliberately flew with an engine inoperative), and in all 4 of these incidents, were most likely fatal because the pilot lost control of the aircraft, the loss of power was merely what set everything in motion. Had the pilot remained in control, the odds are far better than even that the outcome would have been nonfatal. So engine failure shouldn't be the first thing on your mind when flying in a light general aviation aircraft, the first thing on your mind is can the pilot actually fly the plane with any degree of competence. And in the case of this service (which is very definitely against the spirit of 14 CFR 91) the passenger may be mislead into thinking it's only a little bit less safe than an airline because well there's only one engine, while not realising if anything's going to kill them it'll be more likely that the pilot just loses control.