To be

I learn something from Cambridge Advanced Grammar in Use:
appear, seem
After appear (= seems true) and seem we sometimes use to be before an adjective:
• He seems/appears (to be) very nervous.
We include to be before the adjectives alive, alone, asleep, and awake:
• I didn't go in because she appeared to be asleep, (not ...appeared asleep.)
While I find some sentences like the following in A Comprehensive Grammar Of The English Language:
The patient seemed asleep.
Which one is correct?
And why?
Could you native teachers explain it to me?