First and foremost, the (hopefully) double-blinded observers are forced into subjectively anthropomorphizing the behaviors of subjects. And although I am aware I am being ironically anthropomorphic in my reasoning, animals’ usage of mirrors can be attributed to a variety of justifications.
The mirror itself is a novel object in the animal’s environment, and without a proper baseline assessment, researchers may attribute behavior at a mirror to be due to self-awareness fallaciously. The subjects simply be curious by the introduction of a novel stimulus, and perhaps decreased presence in the mirror as the experiment progresses is attributed to desensitization to the stimulus rather than by the presence of self-recognition. By the same token, animals may not have any reaction to experimental marks if they do not in fact resemble anything that might cause for concern in a normal environment. For example, if the mark on the animal resembles a parasite or blood, the animal could potentially be more interested in pursuing its removal. However, if the animal has seen similar marks on other individuals around him and is no cause for concern, the animal could simply be ignoring its presence. This does not mean that the animal does not possess self-recognition; it is simply not displaying the behaviors we are looking for in our assessment of self-recognition. This potential explanation is of course largely anthropomorphic, and I am implying a first- or even second-order intentionality system to provide an alternate interpretation, but I think it is feasible for primates, especially chimpanzees.
Self-recognition is, in my opinion, largely mental and is close to impossible to assess in organisms who are unable to provide personal accounts. As seen in humans, one can possess a mental state without displaying it, and without a sufficient motive or cause for concern, animals may simply not display the behaviors we are looking for. That being said, mirror-guided body inspection can provide us with some valid information about the possibility of non-human self-recognition – but it’s simply not the whole picture.