DG, when I enter Guyana with a US passport I don't have to get a visa that means I am not treated as a "foreigner." A true foreigner has to get a visa.
Based on the agreements between countries.
In the specific situation you have cited, by having a US passport you will not need a visa to enter Guyana because of the agreements between the two countries. However, by entering with a US passport, you are considered a citizen of the US -- hence a foreigner.
Arite I think I would prefer to be a "foreigner" so I can get access to the US Embassy if I need to in case Venezuela tek over when I am there 
Perhaps, a very good choice.
On a personal note ...
I have only a Canadian passport and I am protected by the Canadian government administration where ever I travel.
When I enter any country, meeting with the Canadian Embassy officials to make my presence known is the the first thing I always do. Also, just before I leave, I let them know of that plus my next destination.