@PersistenceContext EntityManager thread-safety in Spring and Java EE

EntityManager is not thread-safe by definition. Servlets specs says that in non-distributed environment and without implementing SingleThreadModel, there is only one servlet instance per definition.

Therefore, in Java EE when you inject an EntityManager through the @PersistenceContext into Servlet's field - it's not thread safe:

public class MyServlet extends HttpServlet {

    // Not thread-safe, should be using EMF instead.
    @PersistenceContext
    private EntityManager em;
}

1. Is this correct to say that even though the default scope of Spring beans is singleton, the EntityManager is thread-safe as the Spring uses ThreadLocal to bind its transaction and EntityManager to it?

2. Is the above Servlets example still valid in Spring? Is it still not thread-safe?

3. Does the ThreadLocal approach works only for Spring managed beans and plain servlet is not one of those?

4. As far as I remember, it's the container responsibility to inject the EntityManager. In Glassfish Java EE implementation, it was the application server who discovers the @PersistenceContext as injection point.
   How does it look like in Spring? Is the Spring Framework responsible for discovering those annotations or it's responsibility of the JPA implementor?