Here's an interesting anecdote on this issue that happened at my place at the end of last year.
I have this instructor, let's call him Randy because that's his name, who outranks me by one degree who likes to drop in and play and teach about 1 time per month or so, as his job (the remnants of NASA) have him on rotating shift work and he can only make it that often. I very much respect this guy's input in the aikido arena, as he was in the dojo on my very first day starting to train in the Tomiki Aikido, and worked with me on ukemi, changing my rough judo stuff into the cleaner, less-impactful aikido falling techniques. He's got a good eye, and a good mind for communicating what may or may not be happening, and his grasp of the underlying principles is a bit better than my own, even after 20 years. I guess, that's the benefit of doing it for 35? Probably. He's had to put up with my own internal struggles to convert hapkido into aikido, which is fun, but not easy. ("Why can't I just punch him in the face right here I know that's not what we're trying to learn, but there's his face, and I've got a free hand and everything...") BTW, I did learn that, later on, you CAN and SHOULD punch him in the face if you've the free hand... but that's another story. I think I almost gave those guys strokes having to deal with my questions. Nice guys, to put up with it.
Anyway, this story...
Randy and I are teaching a couple of lower level black belts a portion of one of the advanced (read older) kata, doing work with weapons. For those who care to look it up, it's Koryu dai san, and we were working in the "Defensive sword," portion, where uke has the katana (boken, actually of course when learning) and tori is open hands only. The very first technique of this... set, we'll call it, is a timing/blending/spacing learning tool. It looks neat, as well, but that's not the point. Uke comes in with the sword, showmen cut (overhead straight down the middle), best to not be in the attack line any longer. To put the cookies on the bottom shelf so I can get on with the story, tori, as good guy, so as to not be neatly divided into symmetric halves, evades the cut, moving in (timing), does a very simple hnd placement block of sorts (distance), completes his turn and throws uke forward (blending) and in the process, when done right, the triggering of the falling reflex open's uke's hands and tori ends up with the sword. It really is amazing, when you first do it right after trying to do it about a thousand times and failing.
Here's the thing. It's MY school, and Randy just keeps himself back out of the main instructor role, so I'm actually running the class (between 8-10 folks). When Randy is there, I am certainly going to take advantage of his experience (as well as of his eyesight, which is way better than my own, so I use that), so I always ask him to work with my 4D and 2D guys, who are working on San kata. I'll take everyone else and keep them working on their stuff. So, Randy takes those guys and they start swinging swords, which looks pretty cool, so I have to continually redirect the attention of the white/green/brown belts back onto their own stuff like a Pre-K teacher when a policeman on a horse goes by the classroom.
Class is moving forward, people are learning to walk and fall, when to walk and when to fall, listening to my admonishments about when to run away, etc. Meanwhile, swish-slash continues for a bit, then that stops and a conversation develops amongst 2D 4D & Randy. Randy, as he does from time to time, forgets that it's MY school, and he just says, "John, I need you to do the 1st sword technique defense from San kata so we can watch something." Sure, no problem. Well, except for the approximate 18 months of rust that's accumulated since the last time I demonstrated this particular skill. Thanks, Randy. I now hear that all movement behind me in the white/green/brown ranks has ceased. Great, now everyone's watching. Neat-O! No pressure.
Next bit o fun is I note that it's Mr. 4th dan who has the boken. This is Scott. Let me tell you about Scott. Scott is 6'8" (2.03m), and he weighs in at a svelte 270 lbs (122.5 kg). THAT is what is coming at me, grinning with some sort of negative intent with what I am certain he is imagining as a red lightsaber.
Ah well, this is what you sign up for, right? Remind me sometime to write the story about "How the body can not distinguish a difference between an adrenaline dump caused by fear of death vs. fear of overwhelming & imminent embarrassment." It's a good one.
Long story short (already messed that up I know), Scott comes in, trying to divide me longitudinally at the median. That sort of thing has always caused me to focus, so I let go, get the hell out of the way and DO. Scott, surprising everyone including me, ends up across the dojo. Cool, I can still do kata.
All Randy says is, "Huh."
I'm like (in my head only) "That's all I get? Just... huh."
2D who'd been watching closely, says "He didn't do it the way you said." Randy grunts.
Scott, getting up, says "It felt fine. Worked anyway and didn't feel forced." Good man, that Scott.
So, I'm forced to ask, "What?" Well we go off into a barrage of aikido talk I won't bore you non-believers with, but it was funny. It boiled down to I opened up the technique with exactly the opposite action of hand that Randy was telling 2d to use. I mean "opposite," as Randy's method was, to be simple, hpalm down, and I come in palm up. He had reasons for coming in palm down, and they are based in the posture-principles, and I thought that right. We replayed what I did slowly, and he asked me to explain hy I came in the way I do, palm up, which was based in fundamentals we talk about all the time in basic movement, i.e. walking. Also correct, Randy thought. My way helps me compensate for my low vision as well.
So, there you go. At least anecdotatally, the above is proof that there is more than one way to "correct." Or, more than 1 way to skin a cat, though I don't know why anyone would want to do that, it be really loud and messy.
We have lots of sayings for this. All roads lead to Rome. There are many paths to Mecca. The cat skinning thing above, whatever. I think that the problem arises in practice when instructors are teaching things which, on their face "appear" to be different from one person's expression to another. This leads beginners, who have no knowledge base with which to compare, into the Land of Confusion. That's a frustrating place to be. I like Gerry's plan above, which is very similar to what I do at my place. I tell people they can learn any variations they want, "But when it is rank demonstration time, I will want to see you do it This Way, as that way indicates competence with a certain underlying thing I am watching to see if you can show me."