First of all, I have never heard of the cases when PhD students have been assigned to supervisors by some committee without asking the supervisors whether they are willing/able to take the job first. The agreement (for general mentoring or for thesis writing) between the student and the supervisor is almost always voluntary on both sides (almost because there are several standard situations when somebody may be officially in charge of new student orientation, etc., but even then I have never seen anybody accepting this position against his/her will).
Second, there are plenty of reasons the student or the supervisor may feel like they may be a bad match for each other and, believe it or not, if one of them feels so, that often means that it is, indeed, so and matching them by force will lead to nothing but a disaster.
Third, you can never tell the true reason why a professor agrees or disagrees to accept a PhD student (an outright rejection may be chosen for more honest and honorable reason than an acceptance by the way: the latter may just come from wanting some extra points for the coming promotion, the grant application, etc. without any genuine interest in the student and may be "biased" in the same way, like "It will help me to have a minority student on my record, so..."). So don't try to guess what the truth might be. It may be anything in both cases and you'll never have a chance to find it out, much less to prove it. On the good side, I should say that if the agreement is made voluntarily (for whatever reason and with whatever initial motivation), most professors would commit to it and try to help the student all the way through.
Finally, there is little point in discussing a situation that neither has arisen, nor is likely to arise.
Just my two cents :-)