'Referencing' an object for the sake of accessing only a small portion of it's proporties/methods is not good practice. It is much better to expose the required functionality, make it static, then do something like:
// Calling a static method
Game1.DoSomething();
// Accessing a static property
int test += Game1.MyInt;
I think the reason why you are seeing XNA code samples referencing the whole object is because a number of XNA programmers do not have object orientated development backgrounds compared to straight-up C# developers, and are thus unaware of best practices for using the language efficiently.