There is a relationship in that skill is required for rank.
No there isn't.
Seriously.
There is no universal requirement for rank at all. None. It doesn't matter what your idealised, romanticised, largely unrealistic beliefs are… while some systems might be purely technical in terms of rank being awarded, that's actually not even the most important aspect in many cases. If you look to traditional systems, ranking is more about hierarchy and authority within a system… which might have skill-based aspects to it… or be about time-in-system… or relationships… or political reasons… or anything else.
Your insistence on applying your own beliefs and idealised imagery on all martial arts, and dismissing anything that doesn't fit it (when challenged on this, you talk about other schools that might let you buy a belt/rank… but you'd "never train there"… doesn't matter fi you would or not, their presence shows that you're wrong… and they're not even the more important example) simply shows a real lack of being able to grasp anything that's already outside your beliefs. There's more of that coming, of course…
So somebody with a high rank is not going to get the high rank without high skills, as I've said countless times.
You can say it as many times as you want, it's both currently and historically wrong.
I would like to point out I've never heard of a college advisor telling a student to shut up and study. Students should and usually do feel comfortable about asking their advisor anything they feel they need to ask about getting a college degree and if its a good advisor, they will do a good job to make sure the student is comfortable asking such questions. An advisor who tells a student to shut up and study probably wouldn't keep their job.
Bluntly, you have not ever, and continue not to have any grasp of what "shut up and train" actually refers to… and this attempted simile of a college advisor is just idiotic. You might as well say that you've never heard of a chef telling you to shut up and cook… and you'd be wrong again.
Assuming that you're meaning a professor, or tutor, or some other form of teacher, rather than an advisor (which would at least be closer to what you're trying to say), then yeah, they do. You want this degree, you do the study. You don't just turn up and have the teacher fill out the test for you, or just give you the answers without you having done some work for it.
But that's still kinda besides the point… so I'm going to try to spell this out for you.
Shut up and train means, simply, that, if you want the skills and answers, they're not found in whining on a forum, gossiping at the school, standing around and hypothesising about it all… they're found in the physical training itself. You want to get a black belt? Stop whining and put in the work. You want the skill? Stop whining and put in the work. You want to understand this technique? Stop standing around talking about what you think it might be, and do it.
Martial arts are "doing" things. Do them.
And, yes, I know this is some psychosis from your past, and you can't do anything about it now, although frankly what you can do (and should) is to let it go… you're never going to change it, and you're never going to get past it otherwise… but you keep bringing it up.
I get it. You wanted to get your black belt in your timetable. You didn't. The reason doesn't matter. You might have known about the form, asking, or whatever bureaucratic lunacy you're blaming, and still not gotten it in your schedule. Deal with it, get over it, and move on.
Seriously, dude.
Shut up and train.