The 'rule' at the site you link to is expressed too generally.
What it should say is:
We do not say
He seemed to be a very annoyed policeman.
when what we mean is
The policeman seemed to be very annoyed.
The difference in the two sentences lies in the discourse context. Before a sentence is uttered, the hearer or reader already has some information about the context. The sentence adds new information to what the hearer already knows.
In the construction Subject + Predicate, the Subject is typically old information, and the Predicate is new information. When the predicate has the form LinkingVerb + Complement, the Complement slot is where we put the new information.
In the sentence The policeman seemed to be very annoyed, The policeman is old information. We already know who the policeman is—you know that even without the preceding context because he is identified with the. The new information which the sentence gives us is the policeman's attitude: very annoyed.
But in the sentence He seemed to be a very annoyed policeman, the old information is he—again, you know that even without the preceding context because he is identified with the pronoun he. The new information is the noun phrase a very annoyed policeman. The new information which the sentence gives us is the man's profession, policeman, along with the fact that he is annoyed.