Only for those projections from camera, which I wasn't doing - that's correct, isn't it?
No your information is not correct. It does work with any 3d textures ive ever tried using (tough it is possible it will not work for maya fluid, even so it easy to force mayas hand). However i don't know what software you use to render (only ever tried this with maya software, mentalray and mtor, renderman studio) with so hard to say for any exotic renderer like say turttle. And will definitely not work for maya hardware. In any case this is is relatively easy to force the look up to actually use any other shape as a base. All you need to do is dump the world space coordinates to a vertex array and feed that data to the position attribute of your texture node*.
The texture is pinned. But that does NOT mean it can not flicker and swim because you have a sampling problem. Its a totally unrelated issue. There are 2 types of things people call swimming, one which is caused by sampling frequency and one which is caused by objects moving trough their texture space. For the same reason you have hard time turning them into textures you would cause the rendered data to flicker and noise out, because they are the same problem. You still need to get rid of excess frequencies.
and created the texture reference before any deformation
Irrelevant, thats what the menu function would do anyway.
- The 3d data does not need to be from your vertex positions by any means, all affine coordinates interpolate the same way.
PS: the reason we learn theory not practice in universities is just this. Only theory can attack this kind of problems, because in practice you can avoid a problem 20 years and be totally dumfounded when you for the first time encounter a issue.
PPS: Its really hard to be specific as i dont know anything about your texture network, or render in general. It might be that your actually seeing compression artifacts for all I know. Increase your texture filter sizes.
PPPS: sampling issues can in general not be brute forced very cost effectively.