On p.82 of JSR 318 , session 4.3.14 Serializing Session Bean Methods:
1."By default, clients are allowed to make concurrent calls to a stateful session object and the container is required to serialize such concurrent requests."
2."Note that the container never permits multi-threaded access to the actual stateful session bean instance"
Sentence 1 means a stateful session object can be access concurrently (or access by multiple threads) and the container can serialize the concurrent requests.
Sentence 2 means the container cannot permit mutlti-thread (concurrent) access the the stateful bean.
I think I can answer my own question.
What the specification means is:
A client can create multiple threads of requests to access a stateful session bean. But the container only allows one thread to access the bean at a time.
Don't get me started about those stupid light bulbs.