As reporters jettisoned cups of tea and coffee and began ransacking their bags for notebooks and pens, the young footballer stared impassively at the table in front of him, upon which tape recorders gathered in the manner of Alfred Hitchcock's birds. He looked like a mouse contemplating a floor full of set traps.
But by the time Beckham quit the scene, nodding as he did so to one or two of the more favoured pressmen, none of the traps had been sprung. Which is to say that the Manchester United midfielder denied he was considering moving to a foreign club to get away from the constant abuse he suffers from opposition supporters - "Beckham Flees England Hell".
And he avoided commenting on the fact that sealing a Euro 2000 qualifying place at Scotland's expense would be one in the eye for his club manager, Sir Alex Ferguson - "Up Your Kilt, Boss!" And he avoided commenting on how his United colleagues might feel if he were to be voted European Footballer of the Year next month - "Best Boy Becks".
These days, Beckham not only takes a dangerous corner, he recognises one. His England midfield colleague Jamie Redknapp has become similarly adept at fielding awkward questions. Asked in the run-up to Wednesday's Wembley match how he kept a lid on the fact that he was married to a pop star - Louise, once of Eternal but now solo - Redknapp replied, reasonably enough: "By not talking about it." Even at the age of 18, Michael Owen was demonstrating the kind of media-resistant powers it took Alan Shearer years to develop.
But what of their international manager? Even in the space of the last seven days, I fear, Kevin Keegan has offered up a legion of hostages to fortune at the prompting of the cold-eyed denizens of the press.
Offered sufficient quantities of rope - as Keegan is on a regular basis - he habitually sets about hanging himself with the enthusiasm of a boy scout demonstrating how to tie a bowline.
The irony of his situation is that he arrived in the job after the previous incumbent, Glenn Hoddle, had been unable to keep some of his more speculative philosophical views to himself.
No one has ever let Keegan forget the moment when he lost his cool during a television interview during the run-in to the 1996 Premiership race - a race his team, Newcastle United, lost to Manchester United, despite at one stage holding a 12-point lead. Keegan, having allowed the wily Ferguson to get under his skin, was left expostulating to camera: "I'd love it if we beat them... I'd really love it." The overall impression was of Matthew Corbett getting really, really cross with Sooty.
As Keegan expressed his internal rage, it was easy to recognise in him the player who, 22 years earlier, had cast his Liverpool shirt to the Wembley turf in disgust after Leeds United's incorrigible wind-up merchant, Billy Bremner, had goaded him into getting sent off during the FA Charity Shield match.
When he was questioned on Monday over how he views his current job, Keegan exposed his inner doubts and emotions with characteristic openness. With painful openness, in fact. Some of his responses, you couldn't help but feel, may one day return like avenging furies to harry him from his post.
Of his players, for instance, he said: "I treat them as equals." Well yes. But football is still an old fashioned business at heart, where The Boss needs to be the boss. And not one of the lads by staying up to watch the boxing with them. Alf Ramsey would turn in his grave...
Almost as discomfiting was Keegan's admission that he had fretted over the idea that an England coach needed to bring something special - technical? - to the job, before rejecting the notion. "It wouldn't be me," he said. It sent out an odd message, at the very least.
As England progress on the low road to the Euro 2000 finals, thanks in part to Sweden's efficiency and the traditional inefficiency of Scotland's forwards, you - well perhaps not you, but certainly I - want to believe what Keegan believes. Namely that sufficient running repairs can be made to the team to make the predictions of ultimate success faintly plausible.
The talent is there, as we keep hearing - but will it be directed? I want to believe it. But I can't. And in my mind, I can't lose the picture of Keegan explaining the bottom line of his current position.
"It's a difficult job," he said. "You have to tell yourself that one day you are going to be slaughtered [his hands measured a space]."
So let's see how long it takes...