Section 29 of the Convention on Privileges and Immunities of the UN requires the United Nations to “make provisions for appropriate modes of settlement of […] disputes arising out of contracts or other disputes of a private law character to which the United Nations is a party”.
This provision mitigates the absolute de facto immunity of the United Nations, and August Reinisch has argued that the rationale of Section 29 is to ensure due process of law and to protect fundamental human rights.
The UN’s position appears to be that the cholera claim is in the nature of a public (rather than a private law claim cognizable under Section 29) due to the political and policy issues it raises. Nonetheless, there is no explanation in the letter itself as to why this should be considered a public law dispute.
One key element of a public law claim would presumably be that the dispute arises between a state and the UN, but in this case it is absent because Haiti expressly elected not to participate in this dispute. Perhaps another rationale is that the claim involves public law because the cholera outbreak arose pursuant to a Status of Forces Agreement with Haiti.
Many elements of a “dispute of a private law character”, however, would appear to be present: the claim itself was essentially one of tort, the claimants were private individuals (represented by an NGO), and the remedy sought was monetary compensation. This distinction clearly troubled the claimants lawyers as well, as their press release makes clear.Haiti Libre has a story about the UN decision, but it's just the MINUSTAH press release. LeNouvelliste has the release also, in French. The report in AlterPresse is in French but Google will translate it fairly well. Inter Press Service News Agency says: UN lambasted for denying compensation to Haiti's cholera victims, but the "lambasting" is mostly the lamenting of the lawyers promoting the case against the UN. Unsurprisingly, MSPP has nothing about the UN on its website.