I have an Assembly(A) which defines a Managed class which has a public constructor that takes two native types.
I have access to the Header files and compiled lib files
make_public will make the the native type visibile to consumers of the assembly where you use it: http://msdn.microsoft.com/en-us/library/ms235607(v=vs.80).aspx. It will not change the visibility in an assembly you reference.
It seems the assembly you referenced should have had either a make_public for the native type, or simply declared the native type public (see Type visibilty for a header Share a header file shared between native and managed clients).
The below page seems to indicate that they should have gotten a warning for writing the method without making the native types public: http://msdn.microsoft.com/en-us/library/ms173713(v=vs.80).aspx
Perhaps you could post the third-party AssemblyAType code to make sure there's nothing else we're missing.