Learn English – I said / have said

There's a lot of confusion around this, and a lot of half-true "rules" are taught.

The actual rule for the present perfect is fairly simple. The present perfect is a present tense, designating a present situation, so it cannot be used with a temporal expression which does not include the present, the moment at which the sentence is uttered.

Consequently:

^okThe directors have met is acceptable, because there is no temporal modifier. This merely asserts that the consequences of the fact of their meeting (whatever those consequences are) are now in play.

^okThe directors have met this week is acceptable, because the temporal modifier this week designates a timespan which includes the present: it runs from the beginning of the current week right up to the moment of speaking.

^∗ The directors have met last week is not acceptable, because the temporal expression last week designates a timespan which lies entirely in the past, ending with the beginning of the current week.

Note, however, that an entirely past temporal expression may be included in a present perfect sentence if it is 'bracketed' with commas or dashes or parentheses; it is then understood as a 'supplement', not integrated into the sentence but added to the sentence as an afterthought.

^okThe directors have met—just last week, as a matter of fact.

ADDED:
DamkerngT points out that you conclude that use of simple past with an indefinite temporal expression is incorrect. This is not the case. The simple past can be used with no temporal or with indefinite temporals:

^okThe directors met.
^okThe directors met sometime.
^okThe directors met before lunch.
^okThe directors met after that.

The only sort of temporal which cannot be used with the simple past is one which cannot be interpreted as lying entirely in the past, such as now or currently or tomorrow.

These distinctions are simply guidelines but not hard-and-fast rules. The shift of tense does not indicate that the event has not taken place.

Let's say that she agreed last week to have lunch with Susan today, to discuss a business proposition. The lunch does take place. She has a sandwich. Susan has soup. If the question is about what she said, it doesn't matter whether the lunch took place or not:

When I spoke with her on the phone, she said she would have lunch with Susan today, and they did indeed have lunch. She's a woman of her word.

Not needing to change the tense when the assertion is still true does not imply the corollary that changing the tense means the assertion is now false:

He said his brother worked in Milan.

His brother may still work in Milan. The shift of tense signals that the speaker is reporting the speech of another, not making the assertion himself.