Which is safer: country road vs highway?
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.