I'm not a Dane, so I may be wrong on this, but I'm pretty sure that there is no implied ownership in this sentence. For example: "Hun siger at hun har smerte i ryggen" which means "She says that she has pain in her (lit. the) back" Since the subject is clearly stated, the ownership is implied. The example here, however, makes no mention of a he, she, or it for the hair to belong to. Thus "the hair" as opposed to "my hair" or "his hair" etc.