One last update.
The question as I understand it has numerous nested questions:
"...if this statement can ever make sense:
"X didn't / doesn't know any music theory and is one of the all time greats..."
"...is the above statement really saying that these guitarist essentially make up chords as they go along based upon intuition and ear alone?"
"...Is this what people usually mean when they claim lack of music theory knowledge? Is this not considered knowing (to some degree) music theory?"
While I completely agree with the person asking the question that it would be "extraordinarily impressive" for some one to "...make up chords as they go along based upon intuition and ear alone" and would like to add that even a prodigy would have had some memory or experience even if it is a tiny amount to produce an impressive result.
Let's consider music like a language. When a child learns to talk it is both learning from the environment and exploring the voice box, and consequently learning how to imitate sounds and make sounds. A child does not immediately know what the words mean until there is an association, e.g. da da = dad.
At some point the child has learned enough to communicate in a language associated with his parents, siblings, and eventually teachers.
Once the child is in school, a formal presentation, a standardization of the language is taught and hopefully learned.
So in turn a musician may learn the language of music by ear, by rote, before being introduced to formal theory or only learn from imitation, hearing and repeating, and further by taking the learned information and building on this a self taught methodology.
The success to either form of learning, only from ear or only from studying music theory is only limited by the amount of time the musician practices what is in his or her mind and translates this to muscle memory e.g. for guitar, the hands.
The key question that an adversary has pointed out so brutally that I have omitted is, "what does it mean to know music theory?" which is not even asked in the original question per se, but in an effort to save my butt here I will attempt to answer.
To know music theory is to understand a formal peer reviewed pedagogical dogma based on the history of western culture musical practices from the Pre-Baroque era until the late Romantic era and up to the beginning of the Contemporary era, roughly pre-1600 to 15 October 1905 in Paris at the premiere of Debussy's "Le Mer" which has often been sited as the beginning of 20th Century Art Music.
This theory rarely covers the following: Jazz, American Blues, Rock'n'Roll, Folk music of Africa, Australian Aboriginal people's music, to name a few world music idioms.
This training is taught in almost every western music school including universities and private institutions such as the Juilliard School of Music or the Eastman School of Music in addition to covering such things as modes, scales, harmony, melodic line, analysis, counterpoint (both tonal and species) but also challenges the student with intensive ear training, sight reading, private lessons on one or more instruments, composition, and playing in an ensemble. Pretty darn near covers it all.
There is nothing missing in this training. If you understand it and you practice what you learn you will have all the tools to perform, compose, and debate anything written in the last 1000 years of western music culture.
Nothing missing ?
Well, if you were Robert Johnson, or Jimi Hendrix, or Miles Davis you might want to debate this.
I agree with Shevliaskovic in that some people have their blinders on and can not perform outside their comfort zone of what they were taught in music theory.
However, I disagree with Shevliaskovic, music is not evolution. Music history does not evolve in a linear way as to be predictable like a land walking fish. No music is after all art, there is no scientific way to explain how human art has changed because human creativity is neither predictable or static. Yes, to say loosely that music is evolving makes sense in that it is growing but the word evolution is too confining. Let's agree that music is a sky with no limit, and the practitioners of great music understand there are no limits or specific directions but only their passion to guide them.
Most people will need to see it before they believe it, but the wisest musician will be able see it because they believe it. You can not create until you see the vision you model in your head.
---- the prologue --
Theory or not to theory.
You don't have to go to Le Cordon Bleu to learn how to cook a hot dog or roast a marshmellow, however, if you want to truly cook up something exciting in a 5 course meal for 250 people, having knowledge and practice will trump theory only any day.
The best [musical] jams are served up fresh, hot, and spicy.
How much does experience factor into a great performance vs. only theoretical knowledge?
There are countless guitarists that have sold millions of albums that have no "formal" guitar training less college level music theory yet they perform wonderfully, creatively, and make lovely music. What gives?
Knowledge from experience, a knowledge that is not only in the musician's head but in this case his or her hands makes a difference. While theory is great as it accounts for how something "was" practiced, knowing the fingerboard and many chords and the ability to create new chords on the fly is something that only the practice can foster.
The X and the Y may have very easily learned by ear or by rote but it is what they practiced that gives them the edge.