I think this is not quite correct:
Database context will not be changed while executing EXECUTE statements. The reason is changes in database context last only until the end of the EXECUTE statement.
Really should be more like:
The database context will only be changed within the context of the EXECUTE statement. It will have no effect on the context in which the EXECUTE statement is run.
Other than that, very good back to basics question. Surprised by the number of people that have missed the question so far.