The assertion came from Gordon Merrylees, managing director of business banking for RBS in Scotland, after spending a day working at Birthsparks under the bank's Working with You scheme.
Former midwife Cassie McNamara launched the company to design clinical products to support mothers during pregnancy and birth.
It was won contracts to supply a product to six NHS hospitals thanks in part to support from RBS.
Mr Merrylees said the scheme, which has seen the bank carry out more than 2300 visits to Scottish firms since its launch two years ago, allows customers to tap into the bank's expertise on issues beyond traditional banking services, for example by making introductions to contacts and offering advice on strategy.
It also aims to foster more contact between clients and RBS staff in traditionally non-customer facing roles such as finance, procurement and corporate security services.
Mr Merrylees said the scheme reflects a "culture change" taking place at the bank. Noting a "real movement" within RBS that is seeing it focus more on customers and less internally, he said: "The key thing here is, what are you [we] doing to help the customer achieve their ambitions?"