Not only is there no data to support this assertion, but I seriously doubt such data could even be gathered on such a specialized sample. First off, you would have to identify a pool of serial killers (which make up, what, about one percent of all violent criminals?). Then, you would have to ascertain their reasons for continuing or discontinuing their criminal tendencies. Lastly, you would have to demonstrate these patterns across both cross-sectional and longitudinal studies.
I'm sorry, but this simply sounds like a just-so statement made to affrim a pre-existing a priori belief.
And so does this. Simply because data does not exist to support a claim does not make it so, nor does the lack of such data prove the supposition is false, either.