Fitness is a statistical property. What 'owns' the fitness isn't the organism, but the genes. They will tend to be more often transmitted so far as what they deliver is better 'engineered' to the needs of the organisms in the environment in which they live. Moreover, fitness exists over and above the properties of the individual organisms themselves. There are three debated ways to construe this.
Fitness can be a relation of genes to other genes.
Whether fitness is a genetic, organismic or system property is a hot topic in modern philosophy of biology. These fall into two camps - those who think adaptation is not enough to explain diversity of form, and those who think that adaptive explanations require more information than one can obtain from either reverse engineering or the ability to generate plausible scenarios. Perhaps it has this trait because its ancestors had it and it has been maintained by selection. Perhaps it has it because it would be too disruptive of the entire genome and developmental machinery to remove it. Perhaps it has it for reasons to do with genetic drift, simple accident, or whatever.