Several thousands of cases were also checked each month to ensure quality control, she said.
Dispatches also pointed to a backlog of cases at the Fos, including seemingly forgotten cases and unopened correspondence.
Ms Wayman conceded there had been periods where the service was under increased pressure from large case inflows and pending judicial decisions (British Bankers’ Association challenging the Financial Services Authority and Fos in 2011; Plevin vs Paragon Personal Finance in 2014).
But she said the length of time people had to wait for answers has come down since then.
She said: "We just don’t recognise these specific claims. But as with all the issues arising from the programme, we will ask for the independent review to clarify the precise concerns raised and for it to consider them.”
She also denied allegations of improper staff training, saying staff were sent through six months of training which included "aspects of the law and regulation, which are relevant to our work. It also covers product-specific knowledge, evidence gathering skills, how we work and the standards we require."
Lastly, Ms Morgan asked for clarification around a visit to the service by Labour MP Rushanara Ali, which the programme said, was stage managed to make the ombudsman look better.
Ms Wayman wrote: "We were very disappointed with the suggestion that we misled Rushanara Ali MP on her visit to the service in 2015.
"We are satisfied that, although of course we wanted to make a good impression, our preparations for the visit were entirely proper and there was no attempt to mislead her in any way.
"I have offered to meet with her in person to provide further reassurance."
Ms Morgan said: "The independent review must consider the Financial Ombudsman Service's approach to decision-making, the assurance process, and the causes of low staff morale.
"The committee will want sight of the terms of reference before they are finalised. The review should be demonstrably independent, all findings of the review should be published, and the committee will expect to take evidence from the reviewer."
She said she would write to Ms Wayman to set out the committee’s expectations of the review, and would consider whether further action is required in response to the latest correspondence.
Steven Farrall, senior partner at Williams Farrall Woodward, said: "The Fos is fundamentally flawed. It is not the rule of law it’s rule by bureaucrat."
But he said calling for a review of cases would only put more cost on the industry not the Fos.
"This is double jeopardy. In the private market were a company to fail so comprehensively as the Fos it would go out of business. Why then is it right that even more wealth be pumped into an existing organisation to get it to sort out problem its failure created.