Technical vocabulary on this subject is as yet insufficient, and there's always a danger in such discussions of bogging down in ambiguous terms; but what the hell, it's worth the attempt. :)
I don't think what you're talking about is a synesthesia thing, because I do it and I'm not synesthetic in the least (not without trying to be, anyway, which is a conscious act of imagination -- different thing). You're talking about a phenomenon very familiar to "creative" people; so familiar, in fact, that I suspect it probably happens in most everyone ("creative" or less so), but most don't notice it. I think those who say a solution "doesn't 'feel' right" are responding to a less conscious (and specifically less "visual") version of the same thing...and while I can't prove it, I can outline what I mean, in a brief analysis of thought processes themselves: ranked most-conscious down to least-conscious.
(1) Conscious thought -- we'll take this (here) as "all conscious experience distinct from 'external input'" -- has both a narrative and a visual aspect, words and pictures. For most people, the words are primarily automatic, but the pictures have to be willed ("visualize a red triangle, point-down"; "picture Aunt Mary with gray hair (or brown), or with a weight gain (or loss) of 100 pounds" -- in the latter examples, people may even say "I can't picture that!"). Most everyone experiences these things constantly; so far, so good. Let's go a layer down.
(2) With sufficient introspection, most people will discover that they have associated specific internal images (often though not always visual -- specific "pictures") with many of their concepts; that is, not just with "triangle," but with "Aunt Mary." These can change, but often -- particularly for rarely-used concepts -- they're identical time after time: "I can't think of [x-place] without thinking of [where I was that day in 1968, (or) Richard Harris singing 'MacArthur Park']," for example. IMO, the actual substance of thought is wordless and unconscious, and our conscious experience is a froth of learned imagery -- words and pictures -- on top of that: something we consciously manipulate (and which not infrequently is used to manipulate us), but which is (again IMO) only the meringue on top of our mental being.* Anyway, there's level two. Next layer down, then:
(3) What you're talking about is beneath that...and what's confusing your friend is that you experience that directly, and he doesn't (or isn't conscious of doing so). You're talking about the liminal (heh) area between truly unconscious (inaccessible) thought, which isn't in verbal or visual form of any sort, and the layers we've already covered in (1) and (2) above. I have no doubt that those who fashion stories and images ("artists") are likelier to be conscious of these levels, thanks to the work they do. This is as true of "popular" as "serious" artists -- cf. George Lucas's answer to the apparently straightforward question, "Did you have all the Star Wars films completely plotted out all those years ago?" Despite the quotation marks I'm paraphrasing both question and answer, and this is from memory, but he replied something like: "Oh, yes." -- then, after a moment, amended it: "Well, the shape of them." He went on to explain, in what struck me as quite tactile terms, that you get the shape or feel of the story first, and the specifics emerge from that shape as you're working. (This is precisely how I work, btw -- it's not a fancy metaphor, but a literal, if internal, experience. My books have a specific feel, shape, even weight to them before I write them; that's how I knew that Topanga would be an absolutely huge novel, years before I wrote it and with no conscious reason to believe that it would need so many pages...nor, for that matter, very much idea beyond the high points of what would be in the book itself. I did not know I'd have to spend several years studying centuries' worth of literature to write the thing -- hence the eventual length to regurgitate what I'd learned -- but despite what would otherwise have been my conscious expectation, I knew, many years ago, that it would be a massive book.)
(4) Finally, there's the literal unconscious: nonverbal, nonvisual, where we really live, from whence our decisions are made, and so forth (and I'd add, "substance itself," but that's just me).
Please let me know if any of this helps; I may (or sure as hell may not) post sometime later about how writers -- consciously and otherwise -- draw on this stuff in themselves, and manipulate it in others, to achieve their effects.
93 93/93 -- AJ
* This was one of Freud's biggest errors, IMO: he exactly reversed this, believing that the unconscious only develops after birth, thanks to repression. I believe the unconscious is how we start, and that we grow a conscious mind as we develop; hence the difficulty of recalling early years.
That said, the scientific community owes Freud a major apology for quietly removing him from the canon. Despite his many and varied errors, and there were plenty, his work revolutionized the world and still contains much of value, particularly on the split between unconscious (actual) motives vs. conscious (invented) excuses for our behavior. Man is the rationalizing animal, driven largely by the unconscious; if we forget that, we lose one of the biggest evolutionary gains of the 19th-20th centuries. The fact is as old as mankind, and stories embody it all the way back; but Freud and his disciples made us look at it, made the mechanism itself conscious.