Sir Andrew, who in November published a critical report commissioned by RBS on its small business lending practices, said the bank's structure "very badly needs to be looked at".
But he stopped short of endorsing the conclusions of an even more censorious report on RBS by government adviser Lawrence Tomlinson, which alleged RBS's global restructuring group (GRG) had deliberately put small firms out of business, calling some of its findings "extreme".
Sir Andrew told MPs on the Treasury Committee: "I would not be surprised if there would certainly be some cases of SMEs (small and medium-sized enterprises) having been treated rather roughly.
"I would rather hope there are no cases that fall into the more extreme category where they have been put out of business."
He said of the claims that 81% taxpayer-owned RBS sought to shut companies to boost its own earnings: "They are plausible in the sense I understand why somebody would make these kinds of assertions."
He criticised the operation of GRG as a separate, profit-making, part of RBS responsible for deciding which firms came under its auspices and whether they should be run down.
He said: "That is flawed."
He said it would be better for the bank's SME lending teams to decide if a firm's finances were irreparable.
With another separation between ongoing RBS lending activity and the operation of those branches that will be hived off as Williams and Glyn, he said that its small business lending activity was "pretty fragmented".
Sir Andrew voiced scepticism that staff at part-nationalised RBS sought to put firms out of business.
"I can see that perceptionally the sort of assertions there are in Dr Tomlinson's report, they sound plausible.
"Equally they are so strong those statements, and the behaviours that gave rise to that happening are so extreme, one wants to think they cannot be true."
He added: "If I had written the report myself I would have wanted to put rather more substance behind what the assertions actually were."
Sir Andrew added: "I think the very great majority of SMEs are comfortable with their relationship (with RBS) and they are being very well looked after."
The allegations made by Mr Tomlinson are being considered by the Financial Conduct Authority. Meanwhile RBS has commissioned law firm Clifford Chance to look at the contents of Sir Andrew's report.
RBS chief executive Ross McEwan has previously conceded that the "pendulum of risk aversion" swung too far at the bank.
But Sir Andrew made it clear yesterday that RBS's problems and failure to expand its small business lending were diverse.
He said that the bank's obsession with building up real-estate lending in the run-up to the credit crunch left it bereft of the skills needed to analyse other types of business.
"The SME lending problems started with the very considerable overemphasis on real estate up to 2008," he said.
He added: "Up to 2008 the cry was 'we want more assets and we want real-estate assets' and the skills needed to acquire real-estate assets are quite different from the skills needed to look at SMEs, where you are having to understand their business, understand their cashflow and so on."
Sir Andrew also said that many experienced staff had been moved from lending activities into GRG.
Meanwhile, managers were "preoccupied with the question of how to survive", he said.
He knocked back the idea that RBS was still fixated on property lending.
"There is no bias towards real estate today, perhaps the contrary," he said.
RBS declined to comment on Sir Andrew's remarks.