No, not at all offensive.
My question was simply inquisitive and certainly not intended as offensive or insulting.
Please do not think, even for a second, that I meant anything derogatory or demeaning in the asking of the question.

This word is used in many ways and the quasi-legal application may not be understood fully by everyone.
For example, I am a native English speaker and I know well over 300 words :), and I have even taught some law courses prior to retirement, yet I've never had the occasion to use, nor much less have never needed to understand, the meaning of the word categorical as used in this collocation.

The word categorical has several meanings and applications, and I was simply asking if English speakers were familiar with the term used in the collocation. I did not say, nor did I imply, that NES's did not know the meaning.

As per other applications:

-  Category Theory in computing science by giving heuristic guidelines for applying five basic categorical concepts: category, functor, natural transformation, adjoint, and colimit.

-  Categorical Algebra

-  Categorical Perception:  Differences can be perceived as gradual and quantitative, i.e., different shades of gray, or perceived as more abrupt/qualitative, as with different colors. The first is called continuous perception and the second categorical perception. 

- Categorical Imperative:  Contextualizing the categorical imperative: Category linkages, technology focus, and resource acquisition in nanotechnology entrepreneurship.

-  Categorical Variables:  The Use of Categorical Variables in Data Envelopment Analysis

-  Categorical Foundations and Foundations of Category Theory

-  Categorical Object Representations:  Matching Categorical Object Representations in Inferior Temporal Cortex of Man and Monkey

Bill Clinton avoided the phrase entirely:

I did not have sex with that woman!

So, do native English speakers know the meaning of this word "categorical" and "categorically"?

A pretty dubious question I think which could be taken as offensive or insulting to native English speakers whose competence and knowledge was put on doubt. 

1) Minutes ago, on the TV news, I heard the precise phrase you mentioned.

Robert Kraft is the owner of an American football team, the New England Patriots. He may have been caught by Florida police in a tawdry scandal. A spokesperson for Kraft said “We categorically deny that Mr. Kraft engaged in any illegal activity."

I agree that the words "categorically" and "categorical" are mostly used in the phrases "categorically deny" and "categorical denial," and very rarely in any other way. 

However, I have heard the adjective form twice "in the wild" in a context other than "denial."

2) It is used in the phrase "Kant's categorical imperative." Since I've never read Kant and only know of it as a kind of catchphrase, I must rely on quoting Wikipedia: "A categorical imperative... denotes an absolute, unconditional requirement that must be obeyed in all circumstances and is justified as an end in itself."

3) There is a classic 1973 book on investing: The Intelligent Investor, by Benjamin Graham. It is often--too-ofen--said that stocks are an inflation hedge. Commenting on this belief, Graham wrote: "On this point we can be categorical. There is no close time connection between inflationary (or deflationary) conditions and the movement of common-stock earnings and prices. The obvious example is the recent period 1966-1970...."

Therefore, when you said they are only used that way, you were being too categorical.