Is it acceptable practice for graduate students to be guarding of their work?
Without saying acceptable to whom it should be, you won't get any good answer. Is that acceptable to you? Is it acceptable to your adviser? Is such a behaviour acceptable in the context of your "contract" with the subject of your research, namely the school you speak about?
Is this common enough that I can cite it as a reason for wanting to avoid sharing the details?
This would be perhaps a bit field-specific, but as far as I can say, this is not a common practice, nor I would accept it if somebody would use it as an argument.
In my opinion, this stance is very much against the purpose of publicly-funded research.
First of all, realize, doing research has a highly ideal objective: generate, advance and maintain knowledge of humankind. If this does not appeal to you, then ask yourself who pays for your research. If it is general public, i.e., taxpayers of the country you reside in, then they deserve to see your results upon request. If it is so, that includes the officials of the school in question. There is your answer.
Secondly, what is the benefit of you keeping the results private? Are you worried about being scooped? On that, see elsewhere on this site and build an opinion for yourself whether that is a real threat.
Finally, as a graduate student, you should be rather happy that somebody is interested in your research. Most of your peers do not get that kind of attention at all.
To sum up: Unless you are paid from a resource which contractually forbids you to disclose your research results, there is no "objective" reason to refuse sharing your results. It will of course remain your freedom not to share them, but in that case you must stand up to your decision and attribute the refusal to your own personal decision without hiding yourself behind some "common practice". Take responsibility for your decisions!