As the Merriam-Webster Dictionary of English Usage puts it:
The argument is a case of fooling oneself with one’s own terminology. After the 18th-century grammarians began to refer to the genitive case as the possessive case, grammarians and other commentators got it into their heads that the only use of the case was to show possession. ...
Simply changing the name of the genitive does not change or eliminate any of its multiple functions.
They also cite a study done in 1940, in which only 40% of the possessive forms were used to indicate actual possession.