I see that I never responded to you after you wrote a lengthy description....maybe I didn't get notified? Either way...No, I think it's the other way around, I think enneagram 4s (and perhaps 3s) have a high likelihood of (mis)identifying with the INFJ type...
I don't necessarily think there's a problem with what you described as the process in which the INFJ receives and provides information and all that jazz you wrote about Fe +Se, or Ni + Ti. But I do not believe that they use Fi.
Also, I am still not exactly sure what specific behaviors you see that make you type someone a certain way. At this point, I don't think it matters either. I can agree to disagree on that cause it's a matter of perception...which is subjective.
But in the chart I linked previously, it clearly shows that 4's are Most Commonly INFJ's and INFP's. And it also shows that 4's, are Less Commonly, but still typed as ISFP's and ENFP's. The rest of the chart shows Least Common for all other MBTI types. So do you not think that is correct?
Take a look at this: Enneagram and MBTI Combined - Renee Baron
I think this clearly shows how some of the functions can correlate with each enneatype.
From that very same book in which I linked you (Which I own) it says on pgs starting at 141-149, what each enneatype tends to lean towards.
One's -predominantly Judging
Two's - prominent feature is Feeling. They also tend toward Extroversion.
Three's - tend toward Extroversion and Judging
Four's - predominant features are Introversion and Feeling
Five's - predominant features are Introversion and Thinking
Six's - correlate with every MBTI type
Seven's tend toward Extroversion and Perceiving
Eights's tend toward Extroversion and Thinking
Nine's tend toward Introversion and Perceiving
Going by any of this...why wouldn't 4's identify as IXFX's?