My grammar book tells me that "present tense" usually cannot be used to represent "one-time action happens in the present time". For example, "He sleeps in bed" doesn't necessarily mean that he is sleeping in bed right now (present action).

But I saw these sentences:

He says that he is busy now.
He says that he will be busy tomorrow.
He says that he has been busy recently.
He says that he was busy yesterday.

Those sentences are examples from one of my grammar books. They are used to explain "the sequence of tenses". I think the verb "says" is somewhat strange here. If they are correct in using present tense, what do those sentences mean? Do they mean that "he is saying..." or other? My concept is that present tense is used to refer to "present states", not "present actions". So I'm very confused with this case. Could you please tell me why they use present tense here? Thank you very much!!
You need to consider words like "say" (reports, indicates, purports, alleges, asserts, and other vebs that are used to relay information) from the types of verbs that actually DO something.

Even so, "he is saying" is what he is doing right now, while "he says" is the general claim he made.
Thanks! That's very helpful.