Not sure about Bulgaria and Cyprus, but in Romania's case having a visa refusal rate of above 3%

From my circle of friends it seems like random chance, and because there is no reason given for the refusal one can only speculate. When I got my B-1/B-2 visa, my interview was very quick (I'd even dare to say closer to 1 minute). Whereas I have a couple of friends that applied for a travel visa and were rejected after being "interrogated" more heavily. When it comes to travel visas, I would assume they would mostly filter for potential illegal immigration, but all those I know that got rejected were pretty well "rooted" in the country.

There might just be the fact that getting an invitation letter from a company is considerably more important than receiving one from anyone else.

Cyprus has a land dispute with the US.

The Americans thought Turkey should run it to avoid them taking up a communist government

There's still un peacekeepers there keeping the conflict quiet iirc