Maybe they’re not “paying” him with money. His reward for the spin is that he gets to live. Not being assassinated is a great motivator.
The spokesman is an agent of the DNC, so he’s not under threat. The family probably has been threatened - they act like it, big time.
I’d guess that he’s being paid not by the DNC directly but rather through some proxy that will give just enough deniability for the NYT to run a “nothing to see here” editorial slamming investigators.