Is it forbidden to speak while the mu'adhdhin is calling to prayer? (Clarification of an issue: Can it be said that it is possible the Messenger of Allah said so and so?)

The questioner: O our Shaykh, even if the command of the Prophet (peace and blessings be upon him) to respond behind the mu'adhdhin were obligatory...

The Shaykh: How? Even if it were what?

The questioner: If the command here were obligatory, does that prevent us from speaking?

The Shaykh: How? You speak and you respond?

The questioner: Yes.

The Shaykh: How is this possible?

The questioner: The mu'adhdhin called to prayer

The Shaykh: No, no, show me how this is possible?

The questioner: The mu'adhdhin says: "Allahu Akbar, Allahu Akbar." I speak after he finishes, I say: "Allahu Akbar, Allahu Akbar."

The Shaykh: First of all, this involves a very clear degree of difficulty.

The questioner : How?

The Shaykh: I will tell you, first of all, you seem to imagine that it is an adhan like ours here, meaning: there is ample time, whereas the adhan there, my brother, the adhan was simple, just as he calls and you say, so you have no room to combine the speech that linguists call "complete speech" with whatever you respond with, whatever you speak, and so on. You are imagining a purely imaginary matter, not a realistic one. This is the first point. Second: if the matter were as you said, the narrator would have mentioned that we used to respond and speak, he would have combined the two matters as they are combined in your mind. And this reminds me of a very important aspect, and knowledge is vast. Many people, when they discuss some issues and stop at some hadiths, say: "Yes, it is possible that the Messenger of Allah said so and so." And I give you an example that I recently came across:
: Do you know the hadith of the Khath'amiyyah woman in Hajj? It is that the Prophet (peace and blessings be upon him), after stoning the pillars, met a Khath'amiyyah woman, and his companion (Radeef) was al-Fadl ibn al-Abbas. He was looking at her and she was looking at him. She was beautiful and al-Fadl was handsome, so the Prophet (peace and blessings be upon him) turned al-Fadl's face to the other side. Then his uncle al-Abbas said: Why, O Messenger of Allah? He said: The subject is related to the issue of the woman's face, whether it is 'awrah and included in the generality of the saying of the Exalted: There is disagreement among scholars, both past and present, which is not our concern here. The subject is that those who say that the verse means covering the face, they counter those who disagree with them with the right, using the hadith of the Khath'amiyyah woman. So what does some of them answer? Here is the point, because the argument with the hadith of the Khath'amiyyah woman is that she was beautiful. So how does the narrator know that she was beautiful? And why was al-Fadl looking at her if she was, meaning, covered in black from the top of her head to the soles of her feet? So she was uncovering her face, especially since, as they say, she was in a state of ihram, and one in ihram is not permitted to wear a niqab, though she may let her veil hang down. So the objection comes from those who say covering the face is obligatory: if covering were obligatory, he (peace and blessings be upon him) would have ordered her to cover her face. Here is the point, what does some of them say? It is possible that the Messenger of Allah (peace and blessings be upon him) ordered her to cover. We say, as came in some athar from Ibn 'Umar: "Make your 'it is possible' at that star." This possibility opens up many problems for us in the narrations: First of all, it means we have attributed to the narrator of the hadith, who is 'Abdullah ibn al-Abbas, the brother of al-Fadl ibn al-Abbas, that he did not narrate the incident to us in its entirety. So why do we say it is possible that the Messenger of Allah ordered her? If the Messenger of Allah ordered her, is this kept secret or transmitted? It must be transmitted. And if it was not transmitted, then he did not order it. I say: this opens up many doors for us. Every bid'ah (religious innovation) that we deny today, our argument in it is, my brother, if it were good, they would have preceded us to it. Yes, how do you know, my brother, that they did not do this thing? Our answer: if they had done it, they would have transmitted it. So then, do we say it is possible that it occurred but was not transmitted? It means: we have ruined our drink and our madhhab (school of jurisprudence) now. I return to the narration in al-Muwatta: if there had been a combination of responding and speaking, the narrator, as you imagine, would have transmitted both matters, but he transmits it as if we were speaking. You can say: speaking does not contradict responding. I say, you are correct, but also speaking does not contradict not responding, so the argument remains standing. This is what I have on this point. What do you have?