Stonborough seeks to play down the way he has taken on the Westminster elite on this issue, but the policeman-turned-journalist-turned-PRO's reputation was built on combat with broadcast journalists trying to dig dirt on his corporate clients.
For a combination of reasons, Stonborough has carved himself a reputation as something of a bruiser. And yet like most stereotypes, the image doesn't quite fit this calm and measured man. I'm greeted in his neat Regency-style Fulham living room by a polite, gently-spoken man who could pass for a younger Richard Attenborough and sounds like Anthony Hopkins.
Stonborough is unabashed when I bring up the legendary baseball bat and its connotations: 'There was a time when every organisation was seen as being corrupt. My role was simply to make sure that reports weren't one-sided.'
Given the coverage of Martin's recent spat with senior Labour figures - and the generally positive way he has been portrayed, despite some unpleasant briefing from within the Labour Party - Stonborough seems to be having the desired effect of raising his client's profile. With almost 14 years in the business, he is well practised.
In the late 1980s and 1990s, it was all too easy to fill a void of defending corporate victims of investigative broadcasts, he recalls: 'The classic example was Shell, which I was doing a major expose on. It was like taking candy from a baby, turning them over. But I eventually realised that these aren't fundamentally bad people, they just didn't understand the game.'
Shell became one of Stonborough's first clients, and has stayed with him, on and off, ever since. Other blue-chips to have used his skills include Airtours, Abbey National and Tesco. But the nature of the work has changed, Stonborough says. He now sees his role as far less aggressive, and more advice-led: 'JS becomes grey-beard! There's plenty of potential in wise counsel, rather than the bruiser approach.'
Stonborough is keen to relegate the baseball bat image to history - the bat itself he gave away at an awards ceremony a few years ago. And there seems to be less need now for his brand of crisis defence. Like the rest of the PR world he has been cutting back - closing his West End office in January and working from his homes in London and Dorset.
But he insists his contacts in the media and corporate worlds have made his slide into more strategic work a painless switch, and this is no idle boast. One current client talks of being invited along to a lunch organised by Stonborough, to be faced with a 'who's who' of directors from FTSE 100 firms and high-profile journalists.
Indeed, ask Stonborough which part of his job he gets the biggest kick out of, and he talks about the great joy of mixing with interesting people and 'being in the thick of things.'
There is no doubt as to his connections. On his mantelpiece he has a picture of himself at a christening posing with, among others, Princess Diana and Sunday Telegraph editor Dominic Lawson.
He plays down his role in A-list circles, but later he mentions that he went to school with Prince Charles and is a great nephew of the philosopher Ludwig Wittgenstein.
However showy he may be about his contact book, he is more circumspect about his work for the House of Commons Commission - and its representative official, Martin - at one point referring to it as just 'a small part-time job that involves strategy for a civil service department'.
Stonborough was first hired to help deal with media interest in the MPs' offices, Portcullis House. But having been the subject of Commons questions over his appointment, he wants to avoid stirring the pot any further.
There is no doubt the Commons job represents a change in style for Stonborough's work. No longer spending most of his time barracking journalists, he is pitching himself more at strategic advice: 'I spend a great deal of time chatting to executives about the British media scene.'
He still does media training, though, taking freelances across the world to give corporates a taste of treatment by journalists. But it would be too simplistic to assume that Stonborough has gone soft just because, in his own words, he's on a steady run to retirement. Under the jovial exterior it's not hard to see glimpses of steeliness.
'He's very charming. We (his clients) all see his nice face,' says Christina Mills, Abbey National head of media relations, 'but I don't doubt he can talk tough when he needs to.'