They are mutually exclusive because they have different sorts of referents. Here's a hopefully clearer example:

• hasty generalization: this brick is small, so all bricks are small.
• composition: this brick is (or even all these bricks are) small, so this brick house is small.

In the grandparent, 'Americans' refers to the people in America, where 'America' refers to the country.

Though the OP does refer to 'America', so I don't know in retrospect which is more appropriate in context.