Interesting topic, Brian. I paint in watercolour and aim to follow the pure watercolour principles. My understanding is that Pure Watercolour painting is the application of just one layer of watercolour paint. So you choose the correct tonal depth for the next brushstroke, and apply it in one go. The idea being that the whiteness of the paper behind the paint can therefore still shine through, giving pure watercolour works that lovely glow, as if lit from behind. If you get the tone or colour wrong, the idea is to start another painting rather than go over the area with another layer, because that begins to dull the light. Also, in pure watercolour, you generally try to only use the white of the paper and not opaque white paint for your whites, although the odd touch is fine.
It's my favourite kind of watercolour because for me it's all about that special and unique clear freshness you get with watercolour. The Pure Watercolour societies' aims and reason for being set up is to promote and educate and keep the tradition going, as many watercolour artists now use the layering techniques to create their paintings. I don't see any snobbery, personally, as they're not rubbishing other styles, only saying that pure watercolour is worth preserving. I personally love it and it really makes me aware of looking for the light and taking care to study tones. That's it, finished. Phew!