First, let us be clear that this response is a general analysis and cannot by itself resolve your quandary. This is because many of the relevant elements can vary from one case to another similar case and because the setting of the army can make the situation unique. The army has the right to make rules of discipline that they (justifiably) expect soldiers to obey, even if the only reason for these rules is to maintain an atmosphere of discipline. The only way to be able to be sure that taking such an object is not problematic in a given case is by inquiring with the proper authority in that setting.[1]
We also emphasize that our response is a theoretical analysis based on the assumptions you provide in your question. It should not be taken as correct concerning cases in which it is not possible to determine the veracity of such assumptions.
We are working with the assumption that the objects in question were, at some point, fully owned by the army and slated for worthwhile purposes. We are also assuming that at the time of the dilemma, these objects were expected to eventually end up in the garbage, at which point they would be hefker (ownerless). There are two possible justifications for using such objects before they are disposed of:
1. The owners give permission: It is a good question whether permission has to be explicit or can even be assumed.[2] Presumably, if an owner refuses to give permission, the one whose request was rejected has little he can do about it, even if he believes the owner will not be adversely affected by his taking it.[3] Granted, there is a concept of kofin al midat S’dom, that we may force a person to allow someone else to technically infringe on his ownership rights when failure to allow it is immoral.[4] According to many, in a case in which we may force an owner to agree, one who wants to use the object may take it on his own accord.[5] However, when there is any semi-plausible reason that the owner might lose out by his object being taken, it is forbidden to take it against the owner’s will, even if his objection is due only to concern about what might possibly happen and even if the potential damage is not a direct, standard type of damage.[6] The reasons you cited for the army not agreeing to take the items suffice such that one may not take such items against the army’s will.
It is plausible, as you suggest, that the reason an entity such as the army does not give permission to others to take their food is not because they really do not want it taken, but only that they wish to protect the army from being sued if someone gets sick. If this is indeed the case, that would change the picture. However, we cannot more than conjecture whether or not that is the case here.
2. The object has already become hefker (ownerless): In general, an owner needs to make an actual declaration in front of others in order for his property to become hefker.[7] However, in a situation in which it is clear to the reasonable observer that the owner has no interest in keeping the object or trying to prevent someone else from obtaining it, no actual hefker procedure is necessary.[8] In such a case, a person who would like to take the object need not be concerned that perhaps this owner is different from the norm.[9] It is possible that even if the owner, for some strange reason, does not want others to take the object (yet), his highly unusual outlook is not halachically significant, and one may therefore treat the object as already hefker.[10] However, if in the case you are presenting, there are rational reasons for the army to not want others to take the objects, the objects are not hefker before some actual process of hefker has occurred.