Mr Narev, fronting a parliamentary committee, admitted CommInsure had wronged some of its customers and apologised for the pain.
He said the bank had put in place a "very significant program" to investigate any deep-rooted issues but denied a culture of bad practice.
As tragic as some individual situations were, the experience of a vast majority of customers was good.
"If we're talking about a period where we've paid 100,000 claims, what I'm not going to do is start reading out the names of the 99,000 people who said they good experience," he said on Tuesday.
"People are quite rightly identifying cases of poor customer outcomes which deserve better - and we agree with that.
"What we don't agree with is the extrapolation.
"Our goal is to uncover any cases where a customer has not had the right experience and put it right, then look in a very detailed way through the business, which we're doing, to identify any broader problems and put that right."
Since changing the definition of heart attacks, for example, CommInsure has paid 17 customers retrospectively.
Mr Narev said the bank had already reviewed five million documents but that there was still work to do.
While investigations has led to some employees suffering pay-related "consequences", no individual has lost their job.
"Because we have not seen the need to do that. If we do, we've got very clear principals on it and we will make sure that happens."
The chief executive was quizzed about a number of well-publicised cases, including that of Peta Outzen, whose family was refused a payout by the company.
Police and the coroner found the woman died of an accidental prescription drug overdose but CommInsure decided she had taken her own life.
The bank boss conceded the claims manager's ruling was a mistake, even though her cause of death was also excluded from the policy.
"Regardless of whether the circumstances of this tragic death would or wouldn't have been covered, that's a process which was not customer-friendly," he said.
The committee has asked the CBA to produce documents relating to its internal investigations of the issue and other relevant papers.
