1 Corinthians 4:
6Now, brothers and sisters, I have applied these things to myself and Apollos for your benefit, so that you may learn from us the meaning of the saying, “Do not go beyond what is written.” Then you will not be puffed up in being a follower of one of us over against the other. 7For who makes you different from anyone else? What do you have that you did not receive? And if you did receive it, why do you boast as though you did not?
The point is this: Do not boast. Do not puff up yourself. Do not go beyond what is written.
A good example of this is found in Genesis.
New International Version
16And the Lord God commanded the man, “You are free to eat from any tree in the garden; 17but you must not eat from the tree of the knowledge of good and evil, for when you eat from it you will certainly die.”
1 Now the serpent was more crafty than any of the wild animals the Lord God had made.
The serpent is puffed up.
He said to the woman, “Did God really say, ‘You must not eat from any tree in the garden’?”
He went beyond what God said.
2 The woman said to the serpent, “We may eat fruit from the trees in the garden, 3but God did say, ‘You must not eat fruit from the tree that is in the middle of the garden, and you must not touch it, or you will die.’ ”
Eve also went beyond what God told Adam.
4“You will not certainly die,” the serpent said to the woman.
Now the serpent got even bolder, directly contradicting the word of God.
Paul's point was to stick to the words of God as closely as possible. Don't add to it. Don't be boastful. Don't go beyond what is written.
Does this mean we are to take the plain and obvious sense of what is actually said, being very careful about making logical deductions from the written text and then attributing to the logical deductions the same force and authority as the original text?
OP: I sometimes say about myself that I say what I mean, I mean what I say, and if I didn’t say it, I didn’t mean it. Is something like this what Paul is saying?
Yes. Stick to the words and wordings as close as possible. Do not put words into God's mouth.