Whether the England coach acquiesced or was already of a similar mind when analysing the situation left by Michael Owen's suspension and merely had his judgement confirmed, 4-5-1 was the verdict, with the captain nominated as the anchor in a five-man midfield behind Wayne Rooney.
It succeeded, in a sense, with England securing three World Cup qualifying points, albeit in an unconvincing fashion against a team without a victory in competitive games in a sequence stretching back two-and-a-half years, and Beckham's performance vindicating - at least from an attacking viewpoint - that supposed deployment of player power. If, indeed, it was.
However, as Eriksson stood, perspiring in shirt sleeves, applauding his men after they had protected their lead during a final hectic 10 minutes of aerial bombardment, even he would have conceded that this victory raised more questions than it resolved - and certainly in the last 20 minutes when his substitutions appeared to confuse everyone, include the players.
Principally, he would have asked himself: is Beckham really equipped to fulfil the holding role? The answer, once the finer moments have been distilled and the sediment rejected, is probably not, even in the context of this confrontation against the 83rd-ranked football nation.
Way back in the mists of time, long before it was deemed that "there are no easy games in international football", Wales would have been treated with something approaching contempt. Well, that's the legend, according to that sage of 1966 and all that, Jimmy Greaves, whose scathing response to Eriksson's latest formation, had been that, in his day, England would play a 1-5-4 system against the Principality, and "use the match for shooting practice - and that against a useful Wales team".
We may scoff at such comparisons with yesteryear, but it was not difficult to assert that Eriksson does offer his critics an inviting target. When he agreed afterwards that England's performance was "up and down", it was an accurate assessment of his men's confrontation with Ryan and the Remnants, as John Toshack's team could be more accurately described. Giggs toiled valiantly and with typical fleetness of foot, as did "Little John" Hartson.
This game always bore the look of one in which England would need to exhibit almost criminal recklessness if they were not to secure a comfortable victory - whatever the formation. They simply possessed too much individual prowess for rivals who had arrived from such clubs as Burnley, Coventry City, Bristol City and Swansea.
Somehow Eriksson made victory a rather more complex a process than it should have been. In the prelude to the game, one could comprehend the Swede's reluctance to promote Jermain Defoe to partner Rooney, and there is, of course, no reason why a coach should not consult his experienced players; it's just that Beckham's participation and ultimate role suggest a somewhat subjective interest. It's a position the Real Madrid midfielder has long hankered for, even though he concedes himself, in defensive terms: "I am not a [Claude] Makelele." Quite so. It is a specialist position, and England's long-term future may be better served by Newcastle's Scott Parker, Tottenham's Michael Carrick or Bayern Munich's Owen Hargreaves.
Beckham reflected of that new role in the England side: "When you've got players like Frank [Lampard] and Steven [Gerrard] around you it is easier. We're professionals and, if you're asked to play in different positions and different styles, you should be able to do it."
In a first half which had followed possibly the most venomous reaction to the "English" National Anthem - why do they persist with this dirge, anyway? - Beckham certainly looked the part, directing his team-mates, like a titled lady instucting her people below stairs. A gesture to the disappointing Lampard here, an admonishment to right-back Luke Young, making his first start for England. Still, at least he exhibited some of the leadership qualities which too often appear to be absent.
Though the England captain failed to demonstrate that he truly is to this manner of football born, he did summon sufficient attacking vision - just occasionally exquisitely so - to suggest that he has some affinity with the holding position, though it was when he drove forward and wide, like the Beckham of old, dispatching one speculative centre just before the break which Joe Cole contrived to head wide, that he was particularly menacing.
After the interval that facet of the game was to the fore once more. An excellent cross-park ball for Wright-Phillips, inside an always slightly spluttering home defensive machine, but the Chelsea summer signing was adjudged offside. But immediately afterwards he found the same player, who fashioned an opening for Joe Cole to win the day, if not the minds of the sceptics. Sky TV's pundit Jamie Redknapp opined: "When you give him [Beckham] the time, he can execute passes like he did with that goal." He added that against the élite, such as Argentina, he cannot be certain of being allowed that time.
That is something for Eriksson to ponder; one of many dilemmas for him in the months ahead.