Ed,
I think you've raised an important point, and I agree with you (even though it is the Agree to Disagree forum, hopefully someone will come along and disagree to sort of spice things up a bit

).
The Native American style flute is basically a whistle. A players embrouchure does not create the note, but an external whistle mechanism does. Unlike instruments like recorders that have a tapered bore, N.A. flute has a cylindrical bore. Basically, no matter how you slice it, a cylindrically bored wooden whistle has limits. The contemporary N.A. flute is basically a modernized folk instrument.
The very limits that it's design imposes on it are the same features that give it a unique and beautiful sound. You can manipulate the "limits" of the instrument to give it certain performance characteristics, but always within certain bounds that are determined by the laws of physics.
Ironically, many players who get involved with the instrument want to bring it into contemporary music--they want to play with other musicians and they need their flutes to be accurately tuned to contemporary definitions (where the note A equals 440 Hz). Most of the reputable contemporary makers offer such flutes, accurately tuning the primary scale.
The problem comes when players start getting unrealistic ideas about what this instrument should be able to do (usually defined by their personal needs). As an example:
About 5 years ago, I got a call from a player who wanted a N.A. flute. He described the flute he wanted me to make, and I'm going to paraphrase his description here:
"I want it to have a full, rich warm tone--really sweet. I want it to be really, really stable on the fundamental note so that I can really wail on it. I have a bunch of flutes that jump the octave if I blow really hard. I need it to have a two octave range and I want the cross-fingered notes to be totally accurate..."
Now, most professional flute makers would look at that and laugh themselves silly! A classic "have your cake and eat it too" scenario. He was essentially asking me to change the laws of the physical universe and make him the Holy Grail of flutes!
I had to break it to him. First, any flute that can play two full octaves accurately is NOT going to be stable on the fundamental. It will be a very, very sensitive instrument and it will likely have a very thin sounding voice. On the flip side, a flute that is very stable and has a rich, warm, sweet voice is NEVER going to play two octaves. Heck, it will probably not play 1.5 octaves.
He finally talked to enough other flute makers who said the same thing that he ended up modifying his expectations. However, I routinely get people asking me if my flutes will play the minor third in the second octave. They say that they expect this from all of their flutes because they have one that does it, and they like that.
Well, Ed is right. No wooden flute of this type is going to play those "in between" notes with perfect accuracy. If it is a minor pentatonic tuning and the main scale notes are dead on, in terms of tuning, then the in between notes will probably be close enough. You modulate your breath to bring them up or down.
At the end of the day you have to remember: It's an open-hole tuned, wooden whistle. It is not a recorder or a silver flute that has been precisely machined and keyed to perfection. It's a wooden tube of widely varying density, subject to all manner of climate variations. They sound amazing, and they have a unique character that no other woodwind can emulate. I think we should praise them for their uniqueness and remember their limitations. That is what makes them fun and artistic.
It's like Haiku poetry. You work within the limited framework, and by doing so you are forced to be creative.