I think you might be missing a point of subtlety. You and other posters have argued that Governments have a large influence on ICANN decision making. I think that is relatively uncontroversial. Perhaps you could thus say ICANN works in partnership with Governments (or indeed private sector players such as Verisign), without stretching language too far.
But to say ICANN is a partnership between Governments and the private sector is surely to misrepresent things. A partnership implies (at least to me) a vountary association of two or more persons (in the leal sense) who jointly own and carry out business (normally for profit). And they tend to have distinct features, one of the most important being that the actions of any one partner bind the others in respect of the business, suject (normally) to a partnership agreement.
So if ICANN is a public/private partnership, exactly who are all of these public and private partners, what have they agreed (under the partnership agreement) and what authority have they given ICANN to bind them? I'd argue the answer is ICANN isn't a partnership - it is a non-profit private company with stakeholders in both the public and private community. And with many of those stakeholders, (pick Governments, pick ccTLDs, pick the at large community), there is a distinct absence of any such agreements - there is no voluntary participation.
Describing it as a partnership between public and private sector lends a credibility to it which it does not (yet) have.