Which is safer: country road vs highway? Asking the park ranger about my planned itinerary, her answer was to take, instead, a 4-lane divided highway with wide shoulder, the argument being that it would be safer than using 2-lane/little-or-no-shoulder country roads. Adding that "people drive like crazy" on country roads.

I've heard the same argument offered by a park ranger at another location.

I personally hate riding on highways, because of the noise but also because this is where the occasional narrows (e.g. bridge, overpass) appears to present more hazard potential, and based on the impression that the difference in traffic volume makes it more likely that a DUI/sleepy driver might hit me.

Anyone would be familiar with a source that would offer some indication of the probability of serious or fatal injury suffered by a cyclist as a function of the type of road?

EDIT

As much as I appreciate the sensible opinions expressed below, I couldn't find any evidence to support the impact of road type on hazard.

The closest that I found is a statistics from the UK comparing built-up vs non built-up fatalities and serious injuries for various types of vehicles. The proportion of incidents affecting cyclists vs motor vehicles driver/passengers is the same, irrespective of the road type. Same for A vs B roads.

Another way to look at this question - none of the reviews on the etiology of cycling mentioned the type of road. Mentions were made about the hazard posed by intersections (car attempting a right turn while a cyclist overtakes on the right; failure to obey stop or light) and dooring. 

Sorry for not providing links to sources - I am on tour and using a phone to post/edit
This is highly dependent on where you live and the driving+riding culture in the area.

For example: In the town I live in (Midwestern US), heading south or south east on country roads is fine -- people are calm and aware for occasional cyclists. Heading northwest its a tossup between the country roads and following the highway. And heading southwest, I'd follow the highway as long as I could.

I've driven along I-40 in Arizona before, and it looked like a wonderful place to bike (esp. near Flagstaff); You could see cyclists on it. On the other hand, other highways may not be good, like I-5 in California from LA to SF (where I doubt it is even legal to bike; if I had to travel along it, I'd rather use PCH 1, depending on the destination).  

You have asked two (presumably) trustworthy people, who should have a good idea of the area and suggest using the highway. I'd heed their advice. This is probably the best way to check itineraries (ask someone who knows). Systems like google maps and stuff sometimes give you shorter itineraries or whatever, but they aren't necessarily safer roads to ride on or not properly verified data. 



Highways have some advantages -- regular traffic flow and usually enough room to ride on the side of the road versus narrower roads in the country. Plus, if you do get hurt on a highway, someones likely to see you. On a country road, it isn't clear. The threat of a drunk/sleepy driver on a wide highway shoulder is pretty unlikely relative to something like being hit by a car on a country road cause someone was driving recklessly and/or didn't see you. A shoulder is effectively your own bike lane (modulo the occasional broken down car), and it's ideal to use if you have one. Only downside is you have to be a little more careful with debris like glass bottles and what not in some areas. 

Plus, on some country roads, you have to deal with wild animals. Less so on highways during the day.