Define neutral.
The context of the conversation was that having the testing body owned and operated by the AFL would not be favourably viewed by stakeholders.
Let's venture into hypothetical land:
A sport's governing body contracts a neutral (owned and operated independently of the governing body) anti-doping agency to conduct testing of athletes at the elite level.
Assume that once upon a time, someone leaked the identity of upcoming testing targets.
If you acknowledged the sport's governing body had nothing to do with the leak, I fail to see how a leak would mean that the testing body was not 'neutral'.
If a testing agency allowed itself to be lent on by a governing body in order to avoid positive findings by leaking targets (or burying results, etc), it would lose all integrity and credibility and thus cease to exist.
Assume this leak became public, and compare the reaction of stakeholders and the public to a similar case where the sport's governing body owned and operated their own lab.
It's probably better for everyone involved, including the AFL, to have an independent body conduct testing.