Post here about all things voice, especially singing voice empowerment (though the main reason I started this thread is that I wanted to discuss what vocal instructors teach the right things and what instructors can just be bulls$%tting you. Also, I wanted to get some tips from people who know a thing or two about singing.)

 - straight posture;

 - straight chin;

 - jaw not moved forward;

 - learning to hold your breath;

 - breathing air into the diaphragm all around your waist;

 - controlling the rate of inhalation/exhalation;

 - playing sports because it's supposed to improve your breathing;

 - trying to resonate more in the mouth than in the nasal cavity;

 - relaxing your tongue, throat, jaw, and lips;

 - imagining wearing a top hat, moving up in the hat;

 - attempting to sing with a British accent (because it's supposed to be a more choral accent);

 - not to worry about lip-rolling (a.k.a. lip-trilling);

 - practicing hand gestures when moving up and down in pitch; 

 - resonating in the front (and the middle) of the mouth; 

 - avoiding stress/anxiety/depression (I'm having a major problem with that one);

 - drinking enough water to keep your vocal chords soft; 

 - sticking with organic foods (I forgot how food can influence your voice).

The funny thing is: she told me not to think ... or at least not to think too much about what I'm doing. ... Huh. 

Then there are people on the Internet (just check out YouTube) who suggest a few things that are opposite of what my instructor told me: 

 - do not imagine you are moving up; imagine you are moving down as you go up in pitch;

 - do practice lip-trilling because that is the thing that will help you hold your breath ... and stretch your vocal range. 

Does that mean I should go to different local instructors (real people) to get a better perspective on singing? How can I tell a swindler from the real thing?

One thing I don't completely go along with in the list is re resonating in the mouth rather than the nasal cavity.  Even if not EXACTLY the nasal cavity, surely the sound is going to rest somewhere in the space between the upper jaw and the nose the moment you raise the soft palate.  Of course, it's entirely possible she decided not to start teaching you to raise the soft palate yet because it's a bit more advanced.  But has she taught you how to keep your tongue rested down below so it doesn't get in the way of your voice?  Also don't really see the relevance of accent here.  The only time how you pronounce becomes relevant is when you modify vowels for high notes.  But again, she may be pushing you to mimic a British accent to discourage you from biting down too heavily on the consonants (in case you do that).

You can use free online videos posted by vocal instructors to SUPPLEMENT your personal lessons; it need not be mutually exclusive.  I would say try it and see if it works and whether it works depends on whether it feels comfortable.  Eric Arceneaux is a good coach among those who have posted their lessons online.  This Felicia Ricci also seems to be pretty good.  If you are interested in more all out rock singing, then Kevin Richards of Rock The Stage NYC.  

In my experience, the first thing you absolutely must master before everything else is singing from the diaphragm.  That's the thing that will ultimately protect your voice from damage during the learning and experimentation process.  But once you have done that, you can learn to rest the jaw, to raise the soft palate and all the other stuff.  I am not a pro but I can hold a tune with ease (not being immodest) and learn songs pretty quickly; have sung in a sort of cultural event in my organisation with about 15 musicians behind me (which is basically a lot of noise to sing over).   Haven't worked out fifth octave singing/screaming but can do ok on soft rock/soul ballads.

I've got nothing else to add other than a "thank you" for the timely reply.