Great debate, guys. I love stuff like this.
I'm thinking that this may distill down to the nature of the decisions we make on the job and how the components of those decisions reflect on cultural definitions of creativity. There's also multiple concepts at stake here - administration, creativity, risk and art - and I think we may be mistakenly conflating them.
Production work, regardless of our occupation within it, requires multiple high-level decisions. The question is whether we are choosing between existing options that we've learned to be reliable based on experience or common sense (analysis only), or choosing between those options and ones that have never been tried before (analysis plus synthesis). The former version of decision-making, more common in stage management, is arguably seen as less "creative" as it involves primarily analysis - the dissection and separation of existing ideas. Directors, designers, actors are seen as more reliant on synthesis - the combination of ideas to create new concepts. The inventiveness that loebtmc mentions is certainly a factor in the decisions of a stage manager - we sometimes have to go pretty far afield to find our options given the diverse situations presented by production work. Our choices as to which tools to pluck from our mental toolbox are the ultimate expression of our own creativity. The question is how much synthesis we actually do, as opposed to how much is perceived as necessary to do our jobs by the outside world. We know that we do a metric ton of synthesis. It is ironic and somewhat humorous to me, though, that the synthesis we do is so far afield of conventional definitions of creativity that the folks generally acknowledged as "creatives" cannot grasp that it is in the same spectrum.
However, as On_Headset alludes, the options we choose from are generally tried & true in some manner, pulled from our own sense of preparedness. We keep our toolbox with us and fully stocked at all times. We rarely would come up with a new and potentially risky idea out of whole cloth to address a given situation, whereas directors, designers, actors are expected to do so. There is an association of creativity with risk, and a cultural concept that risk takers are the most creative members of society. Within the confines of theatre I think we can all agree that we are the least given to taking risks. The risks we do take are not often recognized as such simply because they are so cerebral/intangible. The true catastrophes that could ensue from us choosing to behave differently - ambulances and insurance claims, as OH says - are not as blatantly obvious to those without a predisposition for weighing risk factors in their work.
Meanwhile, art and artistry are slightly separate from creativity, as Matthew mentions. The use of unique materials - painting, sculpture, music, choreography - when combined with the synthesis of new options in decision-making is what generates the socially recognized "art." It requires greater specialization and is seen almost instinctively - although not necessarily correctly - as "more creative." You can understand the difference when you consider the relative "art" and "creativity" required in the composer/arranger/remixer grouping or in the difference between a director of new works and a restager/remounter. You can see it in the phrase "Dr. X raises the field of (some traditionally non-artistic profession) to an art form." I have expressed this concept poorly, I know, but hope I've made my point clearly enough.
Yes, the skills required for stage management do place us on the creativity spectrum, but by that regard so do the skills required for every other job. That will not gain us access to the secret club of theatre artists, though, which seems to be the particular issue at stake here. Arguing that we use creativity or synthesis in our job will not convince the theatrical establishment to consider us as artists. In thinking through the choices that I've made in writing about SM over the past decade or so, I've realized that I've almost unconsciously avoided the use of "art" when referring to stage management. I've called it a craft, a trade, a career, but rarely an art, and personally it feels strange to do so. I think whether we consider ourselves artists or not is a personal choice.
When I was working in the industry I did not consider myself an artist. Creative yes, but not an artist. In fact, I feel like more of an artist for doing tech stuff on this site than I ever did while in the rehearsal hall or booth, and web development is pretty far from the conventional definition of artistry. If the artists wanted to go hang out in their clubhouse I was pretty much fine with that, as long as they gave me enough info to do my job. Artistry aside though, I did consider my role to be equivalent in importance to the rest of the production team, and I think that may be the crux of the matter here as I stated earlier. This is not a question of whether or not we're creatives or artists. I think that this debate actually illustrates perfectly the reason why groups like TCG don't know how to classify us - we don't really know ourselves, and we're the classification experts here. Given that our self-definitions as artists/non-artists/secretaries/80's action heroes/what-have-you even within this thread are so varied, I think what's more crucial is defining our importance in the grand scheme independent of categorization.