The East Rennel issue concerned the "Customary Ownership" of the land (What I called, perhaps misleadingly, above :- "Traditional") rather than private ownership issues.
I believe it was the first (1998) site to be inscribed with such ownership because of problems it causes (in some constitutions at least) over what the "State Party" (i.e. the Central government which contracts with UNESCO to abide by the requirements imposed by Inscription) can actually impose upon the site. The Inscription documentation puts the issue succinctly :- "land in Rennell is owned under the traditional customary system. This situation makes it difficult (but not impossible) for national government legislation to be effective in terms of management"
There was indeed a minor revolt in the WHC
"The Delegate of Thailand stated that although he had no doubt about the World Heritage values of the site, he could not support the nomination at this stage, as it did not comply with the requirements of the Operational Guidelines. He noted that customary land tenure does not automatically guarantee effective customary management and that there are no legislative provisions to protect the site from rapid changes such as tourism, which may affect it. He therefore dissociated himself from the Committee's decision."
There was also an associated issue in that ideally the
entire island ecosystem would have been inscribed, but the documentation noted that "the local communities in west Rennel are not favourable to being included in the nomination at this time"
Matters were made potentially even worse since "The role of the Provincial Governments within the Solomon islands is unresolved at this time because the Provincial Government Act was repealed by the National Government in 1996".
The documentation pointed out, possibly correctly, that there could actually be good reason to hope that environmental protection of a site might be better ensured by concerned local people than by a far away central government!
This all provides quite a nice insight into the difficulties of pursuing inscription in countries whose constitutions and governmental realities are not those around which UNESCO rules were framed. It also touches on another issue we have recently discussed - the "bullying" of "Western democracies" whilst allowing far more worrying failures in other countries to go unsanctioned. The former is much easier to do!
There have been problems with other Pacific sites re "Customary ownership"
a.
Kuk see my review
http://www.worldheritagesite.org/sites/kuk.html for some background on this
b.
Chief Roi Mata's Domain - ICOMOS wanted this site deferred for (inter alia) legal protection reasons surrounding the customary ownership - but was overruled
Re other ownership matters
a.
Horta Town Houses - yes 3 of the 4 are privately owned - only the "Maison and Atelier Horta" is owned by the Commune in which it stands - so Blenheim palace still remains the only fully privately owned site!
b.
Berlin Modernism Housing estates - I checked to see if these were in the hands of property companies (my "Commercial Corporation" example). It appears that 2 of the estates are cooperatively owned whilst the others are/were owned by "companies" (One example is "BauBeCon Immobilien GmbH" - Business Week describes this as "a holding company operating nationwide. It offers property management, construction and building, real estate trading, and urban regeneration services...." - so yes it is a "Commercial Corporation") but these are being "privatised" which I take to mean being sold to owner occupiers.