It would seem that reasonable "due process" would require that if the arbcom is contemplating imposing a sanction on a user as a result of evidence of his misbehaviour presented in the course of a case, he should be notified of this and invited to present his own evidence in the case.
These procedural rights are accorded to the original "respondent" in an arbcom case. If anyone else becomes a "respondent" in course of a case, either as a result of a counter-charge by the original respondent, or through any other evidence presented in the case, he or should be accorded the same privileges.
If the arbcom believes that it is necessary to proceed in the quasi-judicial manner that it has adopted, with "cases", "respondents", "petitioners", "evidence", "injunctions", etc, then it should afford all users the same procedural protections.
But personally, I think the arbcom should abandon its current quasi-judial, excessively legalistic procedure and proceed more informally as the implementors of the community consensus when individuals misbehave according to the policies. I would prefer to see the Arbitration Committee change its name to the Moderation Committee and operate more informally, imposing sanctions where appropriate on any member deemed to have violated policy in an egregious manner. They should not wait for "complaints" and "cases" to do this, although of course members should be able to bring problems to their attention via complaints.
The reality is that (1) the current procedure is not an arbitration; (2) the process of collecting "evidence", etc, simply slows down the meting out of appropriate sanctions, and can be gamed by trolls; (3) all the legalistic posturing by wannabe lawyers makes Wikipedia look childish and silly; and (4) the arbcom is not in any case an impartial panel of judges but are members themselves of the affected community sharing its project (whether they recuse themselves or not), and most probably the sanctions imposed by the Arbitrators are not made solely on the basis of the evidence presented, but also on their personal knowledge or investigation of the facts, and their own assessment of what sanctions the community consensus will favor or support.
--Brian (BM)