I hope this is in the correct place.

If modal verbs are not meant to express facts, why is it that speakers add discourse markers such as "it is a fact that" in the sentence below?

"Even though we cannot say for sure what his ulterior motive was, it is a fact that he must have had one."

"We all know as a fact that nothing will satisfy us until we realize the truth for ourselves."

"...but we all know as a fact that you can and do have all black things with no admittance for whites."

"I know as a fact that Americans should damn-well care what China thinks of them..."
Hello Anon

I'm an English learner from Japan and I don't know much about modals. So I don't think I'm a right person to answer your question. But if you don't mind, give me a chance to throw my two cents worth.

As far as I know there are three kinds of modalities: deontic, epistemic and dynamic. Deontic modality is used to perform speech acts, such as offering, requesting, granting permission, commanding, etc.. When I say to my daughter, "You must come back home by 9 o'clock." I am using deontic modality. Epistemic modality is used to express the speaker's opinion about the truth of a proposition. When I say, "You must be a genius, because you solved such a difficult problem." Here I am using epistemic modality by saying my proposition that "you are a genius" is true. Both deontic and epistemic modalities are connected with the will or thought of the speaker, not the subject. With deontic modality, the modal refers to what the speaker wants to do with the sentence. With epistemic modality, the modal refers to how the speaker sees the proposition. On the other hand, the third category, dynamic modality, is more subject-oriented. "John can run a mile in under five minutes." refers to one of John's abilities; it does not give information about the speaker.

Among the three modalities, what clearly conflicts with "a fact" would be the epistemic modality. "Must" in #1 is no doubt an epistemic modal, and consequently it cannot be happy with "a fact". "Will" in #2 and "can" in #3 are dynamic modals and there is no problem for them to go with "a fact". To me "should" in #4 sounds to be deontic, but I'm not sure whether a deontic modal can go with "a fact" or not.

Please wait until our moderators give you more definite answers.
Hello Anon.
I haven't gotten any concrete opinion yet, but your question and paco's answer are interesting. I basically have nothing more to add to paco's answer. But could I put my first impression?

I think, we can〖know〗something only〖as a fact〗, don't we?

(I'll check my textbooks on modality if there's some help...)