Seek “disconfirming evidence”
The strange thing about most reference calls is that by the time the hiring manager is calling she is often already pre-disposed to hiring the candidate. Most people delay reference calls until that point both due to expediency of time (why make phone calls unless you think you might hire the person?) and in fairness to the employee (why call a bunch of people and then not hire him – leading others to wonder why he didn’t get the job?).
I agree with the goal of waiting until late in the process. But the problem is that by the time you actually call people you really WANT to hire the candidate. So often people who do reference calls ask softball questions. That’s not your job. Your job is to seek “disconfirming evidence” meaning you go in with the assumption that Stacy is great but you want to be sure there isn’t something you totally missed.