Can the heaviest edge ever be in an MST? Is it true that the heaviest edge in a directed graph can not be in the MST of that graph?

I don't think it is true because we might end up with a heaviest edge that is not part of a cycle. 

Can anyone confirm?
No, it is not true. Consider a graph with 2 vertices and an edge between them. This is the heaviest edge, and it will be in the minimum spanning tree of $G$.