Short answer
On the basis of a cursory literature review, I conclude that Jospeh's observations were correct, but his conclusions that a callosotomy can result in a dual consciousness were far stretched.
Background
First off, I'm not an expert on this topic, but I will give my referenced opinion anyway, as there is no answer yet to this question; Below are quoted the two sections from the wiki Dual consciousness (neuroscience), as linked in the question:
Rhawn Joseph observed two patients who had both undergone a complete corpus callosotomy. Joseph observed that one of the patient’s right hemisphere is able to gather, comprehend, and express information. The right hemisphere was able to direct activity to the patient’s left arm and leg. The execution of the left arm and leg's action as was inhibited by the left hemisphere. Joseph found that the patient’s left leg would attempt to move forward as if to walk straight but the right leg would either refuse move or begin to walk in the opposite direction. After observing the struggles of the execution of activities involving the left and right arms and legs, led Joseph to believe that the two hemispheres possessed their own consciousness.[16]
Joseph also noted that the patient had other specific instances of
conflict between the right and left hemispheres including, the left
hand (right hemisphere) carrying out actions contrary to the left
hemisphere's motives such as the left hand turning off the television
immediately after the right hand turned it on. Joseph found that the
patient’s left leg would only allow the patient to return home when
the patient was going for a walk and would reject continuing to go for
that walk.
First thing to note - he describes two patients and only one of them is highlighted on the wiki; hence, this is a case report (Joseph, 1988). Case reports can't control for any other personal characteristics of that one patient. Such anecdotal reports are important, but they may not be a reflection of the population as a whole (i.e., people with a transected corpus callosum).
Secondly, the term 'consciousness' is a loosely defined and debated one. Similarly, the 'mind' is a broad and ill-defined term.
Then you proceed to scrutinize his work as based on his unconventional beliefs on the origin of life as based on a rational wiki page. Although his ideas on this may be unconventional, that doesn't mean he has reported flawed observations during his professional career as a neuropsychologist.
However, and I quote a part of the Discussion section of Joseph (1988) where he describes anecdotal behaviors of 2-C:
[He] became angry with his left hand, swore and expressed "hate" for it, struck his left hand/arm with his right hand, and engaged in physical struggles with his left extremity, the right attempting to force the left to comply with some particular activity or to cease to act in a manner that the left hemisphere found objectionable or annoying. [...] In general, these findings indicate that the isolated right cerebral hemisphere of 2-C was able to understand and follow certain simple verbal commands, obtain and maintain knowledge [...], as well as respond, make decisions and act purposefully- even when his left hemisphere had no idea as to what information the right possessed and why it was behaving in a particular manner. Given the differential behavioral observations with regard to the activity and responsiveness of the left half of their bodies, it appears that 2-C (unlike 1-C) is possessed of two minds, one of which resides within the right, the other within the left cerebral hemisphere. Nevertheless, it appears that 2-C's left hemisphere remains predominant in regard to most expressive activities.
The bold text is probably what fueled the wiki article. To me, personally, the 'hatred' and frustration of C-2 is easily explained by the loss of body control. Who wouldn't feel frustration and resentment to that side of the body?
Indeed, a paper by Andrew & Akelaitis (1945) explains a similar behavior by their (partial-)split-brain patients with diagnostic dyspraxia. These authors explain the phenomenon not by a dualistic consciousness, but 'simply' by an unbalanced inhibitory influence of the dominant hemisphere over the non-dominant side. This decreased inhibitory control was hypothesized to lead to the uncoordinated behavior on the non-dominant side. These symptoms generally diminish over time, as the brain deploys alternative inter-hemispheric routing of communications. This sounds more plausible to me.
Lastly, there is a a publication that coins it "alien hand syndrome" (Feinberg et al., 1992). They too, ascribe the phenomenon by a disturbed inhibitory interhemispheric control, and I quote:
Callosal AHS [alien hand syndrome] is best explained by hemispheric disconnection manifested during behaviors requiring dominant-hemisphere control.
So I conclude form this quick literature review that Joseph ascribes the presence of two minds based on something that can be explained at a more basic level, and hence by a more simple model, namely disinhibited motor control. Given the principle of parsimony, I conclude his observations were right, but that his conclusions were not.
References
- Andrew & Akelaitis (1945) Am J Psychiatr; 101(5): 594-9
- Feinberg et al., Neurology (1992); 42: 19-24
- Joseph, J Clin Psychol (1988); 44(5): 770-9