No, it isn't unanswerable. We already know that the heritability of criminality is somewhere near 60%, and that people at the greatest risk for developing criminal tendencies are those who themselves have a genetic predisposition towards crime and are raised by criminals.
An interesting point about genes and environment can be illustrated by turning to a different trait: IQ. Psychometricians studying the heritability of IQ were initially surprised to find that the effects of the environment declined with age. The explanation I've seen for rising heritability is that, while young, people passively accept the environment that surrounds them, and this environment affects their IQ scores. But as people age, they increasingly seek out environments which resonate with their inner nature, choosing friends who are like themselves and hobbies and occupations which fit their character. These new environments also affect their IQ scores, but in a way that brings these scores closer to a theoretically "essential" score which would be assigned purely on the basis of genetics.
What this suggests is that the environment clearly can effect outcomes, but that people will seek environments which reinforce outcomes their genes "want." Hypothetically, if a government were to prevent delinquents from congregating together, using one another as role models, and learning how to lead a criminal lifestyle, this might drastically reduce crime. Unfortunately since criminality is known to be hereditary, this might entail breaking up families.
A better way might be to enforce solitude in prison, and give offenders a choice of three people to interact with. These "prison buddies" could be drawn from a list of dozens in the area chosen on the basis of, say, low scores on Hare's psychopathy checklist. Interacting only with these people via letters, telephone, and visitation, would theoretically help to instill prosocial norms rather than reinforcing antisociality through interaction with other convicted criminals, as occurs right now.