I am a beneficiary of this hedge fund so I may be biased, but I feel pretty confident that there is not much conflict of interest going on. As has been attested to by multiple people on this, and other, threads, there is very little proprietary information sharing between teams at McKinsey. In fact, once you work for certain clients, you are automatically barred from working for others. I was once privy to a situation where a consultant working with a different client, unknowingly, shared some proprietary information with the team I was working on. I saw the extent to which the partners freaked out and tried to correct the situation. Of course, there are examples of people violating this trust (people will be people) but there have not been any examples of structural violations (ie the firm designed processes that encouraged or tolerated unethical practices)
It does McKinsey, as a firm, very little good if their clients' business goes down in flames. They, obviously, cannot bet against their clients (it would be catastrophic to their core business if this was ever publicly disclosed) and so they can only bet with their clients, even if they (unethically and possibly illegally) used their clients proprietary information to trade.
It feels to me that there are some corporations that newspapers can just bash confident that most of their readers will nod along without applying much critical thinking. I understand the skepticism. I used to share it before I got to see the inner workings of organizations like this. There is much to criticize about organizations like McKinsey but violating clients' trust is not one of them.
One last argument against the insider trading inference, the results I have seen, while good, are not indicative of what is possible if smart people were truly trying to take advantage of their knowledge of the inner workings of the largest corporations in the world.