The Present Progressive and “to see” etc.

In Longman's texts Talking about the present, and Talking about the Past it is claimed that some verbs cannot be used in the present and past progressive. But they can. Here is the list of verbs it is calimed that cannot be used: (to) be, have, see, believe, like, agree, know, love, disagree, recognize, hate, mean, remember, prefer, need, understand, want, deserve, wish, belong.

Now consider these commonly used sentences:

E1. She is seeing another man.

E2. She saw another man.

Clearly then the verb “see” can be used both in the present and the past tense.

Consider these sentences:

E3. I am standing here and agreeing with you, but then you give me that. That was uncalled for.

E4. I was standing here and agreeing with you, but then you give me that. That was uncalled for.

It seems to me that there is nothing wrong with these sentences. So the verb “agree” can be used both in the past and in the present.

Consider these sentences:

E5. I am being very nice to you.

E6. I was being very nice to you.

Again nothing seems to be wrong with these sentences. Sentences like (E5) and (E6) seem to be used to stress the act of being nice to someone. Perhaps someone who denies it is the case.

I'm undecided as to which of the other verbs mentioned that cannot be used in the progressive form.