It is, of course, not strictly true. Jorge Burruchaga was a pretty decent midfielder who scored the winner in the final against West Germany while Jorge Valdano, a two-time Primera Division and UEFA Cup champion with Real Madrid, walked away from that tournament in Mexico with four goals to his credit.
If the Albiceleste are to regain football's most sought-after trophy for the first time since that thrilling five-goal triumph over the Germans in the Aztec Stadium, chances are that labelling it another one-man show would prove disrespectful to some better-than-average professionals. However, for the moment, at least, everything depends upon Lionel Messi.
Without him and his four goals, Alejandro Sabella's side would not have escaped from Group F. Without him and his criticisms, the head coach might still be persisting with the 5-3-2 system that led to an abject display in the first half of the team's opening game 2-1 win over Bosnia & Herzegovina.
Without him and his left foot, Argentina would have joined Scotland in the exclusive group of countries who have made one almighty ricket of it against Iran.
Odd as it sounds, considering he is level with Neymar in the race for the Golden Boot, Messi has not produced his best. He has been seen, generally, in flashes. Admittedly, those flashes have been enough to change the course of games irrevocably, but he has been facing his own difficulties in an Argentina line-up struggling to live up to much of the pre-tournament hype.
Yesterday's entertaining, albeit flawed, 3-2 win over Nigeria in Porto Alegre was probably his most complete performance yet, even though it only lasted for 63 minutes before he was replaced - in one of the biggest surprises since Mauricio Pinilla turned up at the tournament in a Chile strip - by Ricky Alvarez.
Perhaps this was, in part, Sabella attempting to show he is not being held hostage by the dressing-room. Even though everyone has stated publicly that he, alone, decided to switch from 5-3-2 to 4-3-3 at half-time against the Bosnians, rumours remain strong that he was bullied into it by Messi and other players.
While he kept the captain cocooned in cotton wool for the knockout stages, it also proved to be an instructive move by showing us just what this side is capable of without him in the ranks.
By the look of it, the answer is: not an awful lot. They lacked real creativity and invention and presented Efe Ambrose, the Celtic defender, with a golden opportunity to make it 3-3 with just four minutes remaining. Sadly, that 'curly toe' spoken about by Neil Lennon in his new role as a television pundit came back into play and he sent his shot into the side netting at Sergio Romero's near post.
Taking Messi out of the action was a bit of a gamble. With Bosnia beating Iran comfortably, Argentina were through. However, two goals from the Nigerians would have relegated them to second place in the group and the potential pitfalls that can deliver.
As it is, Argentina do still have a chance in this competition. Any side in any competition with Messi in the team can harbour some hopes of coming out on top.
But if his nation are to go all the way in an ever more complex and fascinating competition, a number of other players - the modern-day Burruchagas and Valdanos, if you like - really have to start stepping up to the mark.
Angel di Maria came into the World Cup on the back of a terrific season with Real Madrid. He provides excellent attacking support to the front line on the left side. The Nigerian goalkeeper, Vincent Enyeama, can attest to this.
He was forced to make a handful of saves from the wing-back's dangerous shots from distance. With Argentina finding life so tricky right now and toiling to find any real degree of fluidity, he has to maintain the work rate shown in the Estadio Beira-Rio and bring just a little more of his quality to the party.
He is one of the few giving Messi the assistance he requires.
Gonzalo Higuain has a good pedigree. The Napoli striker missed the opening half of that win over Bosnia amid talk of an injury, but he has not looked anywhere near dangerous enough in the action that has unfolded since. He looked tired and mildly despondent, to these eyes, as he sloped off to make way for Lucas Biglia in stoppage-time.
Sergio Aguero, whose season at Manchester City was punctuated by injuries, hobbled off after 38 minutes. He has been another disappointment so far. Indeed, his replacement, Ezequiel Lavezzi of Paris Saint Germain, may be someone Sabella will opt to call on more regularly.
His corner set up Fernando Gago for the rather fortuitous finish that ensured victory and he did reasonably well. He was not brilliant, but, by the standards of a number of his team-mates, he was not bad.
There are undoubted questions to be asked about Sabella's defence as well. Nigeria showed that up in technicolour.
On paper, three wins out of three is what was expected. The games have been decidedly different from what we might have imagined, though.
No-one can win World Cups entirely on their own. That is why Argentina don't look like winners at the moment. Messi, mercurial as he may be, needs a fair bit more in the way of back-up.