Given a basic repository interface:

public interface IPersonRepository
{
    void AddPerson(Person person);
    List<Person> GetAllPeople();
}

With a basic implementation:

public class PersonRepository: IPersonRepository
{
    public void AddPerson(Person person) 
    {
        ObjectContext.AddObject(person);
    }

    public List<Person> GetAllPeople()
    {
        return ObjectSet.AsQueryable().ToList();
    }
}

How can you unit test this in a meaningful way? Since it crosses the boundary and physically updates and reads from the database, thats not a unit test, its an integration test.

Or is it wrong to want to unit test this in the first place? Should I only have integration tests on the repository?

I've been googling the subject and blogs often say to make a stub that implements the IRepository:

public class PersonRepositoryTestStub: IPersonRepository
{
    private List<Person> people = new List<Person>();
    public void AddPerson(Person person) 
    {
        people.Add(person);
    }

    public List<Person> GetAllPeople()
    {
        return people;
    }
}

But that doesnt unit test PersonRepository, it tests the implementation of PersonRepositoryTestStub (not very helpful).