MN makes two important distinctions.
1. Pistols are treated differently than long guns, and
2. Carrying is treated differently than transporting.
A "Permit To Carry A Pistol" (see 624.714) grants the holder an exception to the assumed crime of carrying a pistol in a pubic place. It only directly covers pistols. "Rifles and Shotguns In Public Places" (see 624.7181) also grants an exception for carrying long guns to those who have a Permit To Carry A Pistol. The Permit To Carry A Pistol doesn't authorize carrying long guns in public. It is not a Permit To Carry A Long Gun.
Transporting is another, separate question. Generally, firearms of any kind may not be transported unless unloaded and cased or trunked (see 97B.045). There is an exception there for handguns carried in compliance with 624.714. There is no such exception for long guns. Long guns must always be unloaded during transport. With long guns, once you get in your vehicle, you're no longer carrying, you're transporting. Make sure it's unloaded.
All that being said -- sure, you can lawfully carry a rifle in public on your person in MN if you have a PTC, I just think you ought to have your head examined if you actually do. Just because it's lawful doesn't mean it's smart.