both
The traits I was born with are why I have perceived my life experiences in the way that I have. It would be difficult for me to say who I am isn't the product of genetics with what disorders I have, but a lot of who I am is the product of my past experiences.
I believe that both apply in the case of APsD particularly.
With the right set of circumstances an individual can be made - that applies to traumatic childhoods and to the systematic deconstruction of a moral or ethical code of an adult. I'd imagine this would be easier if the individual had a pre-disposition towards a PD of course, but generally achievable given sufficient time and resources.
I also believe that those that are 'born this way' are strongly influenced by the socio-economic and familial environment they develop in. The anecdotal evidence to date - based strongly on Dr Hare's most learned writings - implies that, generally, an abusive upbringing teamed with low socio-economic status and limited opportunities tends to increase the propensity towards violent crime and contact with the criminal justice system.
A more balanced childhood, with greater academic, social, sporting associations and a higher socio-economic status tends to lead towards the development of your corporate sociopath. Hence, they notably absent from Mr Hare's studies.
On a personal note - I am born the way I am. I had a supportive childhood with a large number of family members, no real mental health issues of note in the family history and excellent educational opportunities.
I am who and what I was born to be. 