Well picklefish, I don't think there is any "one best way".  Different styles of music and playing and different objectives may need somewhat different gear and techniques.

I'd say you've got it with that one rule.  "Make is sound good!"

There an old saying that goes something like "All education is just preparation for action." 

What you do with it is what counts. 

And maybe what he learned on his dad's knee was enough for him to just take it and run with it.

I mean, education is good, when you can get it.  But it is not everything.

Some of it does matter, or at least there are generally harder and easier ways to get the job done.  Sure, there is more than one way the bow can be held.  At first, the Franco-Belgian hold seemed really awkward to me and I tried some others.  But various players from FM to Perlman use it, so obviously it is one of the ones that definitely can work.  When I started working on things like playing for 20 min or so straight without stopping at all, I ended up settling into it because part of why it works is it is one way to hold the bow and get the notes where the right hand doesn't start to cramp up or get fatigued as easily after a few minutes.   But I don't know "proper" from a hole in the ground.  Nor do I care if anyone says I'm holding it properly.  What I care about is that I can do what I need to do with it, and my hand stays comfortable.  I've seen FM's and Perlman's and many other player's videos on it, but I consider it more like friendly advice from experienced players more than a rule or the only "proper" way. 

Fingering, well, you kinda lost me there.  The only real "proper" I can think of there is if it has the right intonation and tone and if you can get to it effectively from where you are and get to the next note ok.  Intonation is just the frequency/pitch of the note.  That kinda has to be right enough, I guess, to be proper.  But say you need to play the first A on the D string.  In first position you'd play that with your pinky.  But is it somehow improper to shift up a bit so you can play it with your 3rd or 2nd finger?  I never knew!  LOL  I would think of that as just "shifting positions".  If you even think in terms of "positions" when playing.  I don't.  The only way I can see of that being maybe bad is if you do it to avoid practising with one or more of your fingers.  Having one or more fingers that are "weak" that you have to work around is never going to be an advantage that helps playing.  That isn't about being "proper", though, it is just sense.  With only 4 fingers, if you are kind of avoiding using 1 or 2 of them, it limits your playing.  I mean, somebody that wants to learn to type fast wouldn't cut off a few fingers, it just doesn't make sense. 

Tone from the left hand, there's a difference between the sound if you just barely press down enough to get the note to sound and a little harder than that.  If you just touch the note with a little pressure you get a slightly softer tone because the flesh at the end of your finger will damp string vibrations a bit.  But both those sounds are proper, so far as I know, so long as you are getting the one you want when you want it. 

With the two violins in the video, I thought they were both really nice.  For different sorts of situations.  They talked about that.  But that didn't make one better than the other.  Personally, for what I *like* trying to play, I liked his fiddle a bit better so far as sound.  But that is personal taste and doesn't make her violin wrong at all.

The whole "proper" thing, I'll take an example from guitar, even though that annoys some folks here because they don't seem to see two stringed instruments as being similar in some regards.  I've been playing for over 30 years.  Not claiming to be great or anything, but I've played in bands and some people over the years have liked my playing.  There will be times for certain moves where my thumb may not be on the "proper position" at the back of the neck.  There may even be times when I will use my thumb to fret notes on the low strings, because all 4 fingers may already be busy.  If someone criticizes that as not being "proper form", I can generally bet they have only been playing for somewhere between 6 hrs and 6 months.  If they had been playing longer, they'd already know that there are some things you can only do by breaking "proper form" and that many of their "guitar heroes" do the same things.  But you don't want to play like that all the time, because it can make other moves more difficult. The "proper" position with the thumb on the back of the neck only seems awkward at first.  It really is better/easier for doing most things.  So when you are showing stuff to someone who is just starting out, that is what you show them, but more because it will be better for things like barre chords and most scales than wrapping the thumb around the neck.  

I've gotten long-winded on this, but basically while I agree with you that there is no "proper" beyond getting the right sounds, the usually recommended ways are often best for the greatest number of situations.  That is why the experienced players are using them at least most of the time.  No sense in re-inventing the wheel.  But that if one is using "improper" ways of playing to cover or keep a weakness in a finger or whatever, it isn't going to help in the long run.  "Basics" are called basic because they are good building blocks to have to work with.