The joke was that Ray Houghton couldn't actually head the ball, that his goal in Stuttgart was some kind of aberration, a suspension of reality.
Yet, Jim O'Kelly's iconic front-page picture in that Monday's Irish Independent conveys a graceful, almost balletic quality, Houghton leaning and watchful as the ball loops wickedly over the heads of England's suddenly panicked defenders. The headline above it reads 'Jack's Trumps - Wild delight as the nation toasts historic victory' so 30 years later it's entirely appropriate the team should be honoured as Irish Independent Sportstar Hall of Fame inductees.
Ireland was a grey place back in 1988, struggling to find beauty in small things. A crippled economy, threatened bank strike and the North still under the sinister shadow of gunmen, it sometimes felt as if the island existed in a gloomy half-light, perpetual dusk almost. Then a group of footballers went to West Germany and, for six extraordinary days in June of '88, this great sunburst exploded across our skies.
Thinking about it now, the lucky twist that sent Jack Charlton and his team to that summer festival (Gary Mackay's goal for Scotland in Sofia) had been such a deviation in what was long considered a natural condition for Republic of Ireland teams - suspicion and self-pity - perhaps we were psychologically programmed to interpret Houghton's sixth-minute goal in the Neckarstadion as an act of folly.
This, after all, was an England side enriched with the creative forces of players like John Barnes, Peter Beardsley, Gary Lineker and Chris Waddle.
Ireland had never won a competitive international against England, but we'd all but written ballads about a friendly victory at Goodison Park in 1949, flickering images of which had been captured for posterity by Pathe News.
Now, even with one of their World Cup-winning team of '66 in our camp, expectations had been resolutely modest approaching kick-off in Stuttgart.
This despite Charlton's team going to the tournament on the back of a 10-game unbeaten run and goalkeeper Packie Bonner not having conceded a goal in more than five and a half hours of football.
There was a biting sense, too, of historic old turf wars still looking to tug people away from any hope of looming romance, the recently-installed GAA president John Dowling declaring that he would not watch any of the action from Euro '88 because he did not "like soccer as a game".
Bonner, a product of Donegal GAA stock, would be quite magnificent against the increasingly flustered English attack that day, eventually extending his 'clean-sheet' stretch to a scarcely believable 729 minutes and decanting a sense of national euphoria expressed in congratulatory telegrams sent to the team by Taoiseach Charlie Haughey and Opposition leader Alan Dukes.
And as the players then decamped to Hanover for their second group game, against the Soviet Union, a parallel narrative began to unspool.
As images of mounted riot police being called in to contain outbreaks of violence between English and German hooligans were broadcast across Europe, Irish supporters were being lauded for the curiously odd condition of behaving like civilised human beings.
England would lose all three of their games at Euro '88, their supporters issued with free rail tickets just to get them out of Dusseldorf after a 3-1 loss to the Dutch.
The same day that was happening, Ireland produced a performance for the ages against the Soviets, one almost scandalously short-changed by a 74th-minute Oleg Protasov equaliser after Ronnie Whelan had scored, arguably, the most spectacular Irish goal in history.
Interviewed on RTÉ television afterwards, Whelan wore a Soviet shirt.
Asked who he'd swapped his Irish jersey with, Ronnie grinningly replied "Something-ov!"
Money, inevitably, became part of the debate now too with revelations that the players would receive bonuses of £5,000 a man if they reached the semi-finals, £10,000 if they made the final and an eye-watering £20,000 each if they won the cup itself.
Pie in the sky? Suddenly, it didn't feel it that day.
The Hanover draw established Ireland as a 4/6 bet to make the last four, their final group opponents Holland having lost their opening game to the Soviets.
And the BBC, sensing a rising tide of dismay with England's now flaring hooligan problem, decided that Ireland's unlikely bid for glory in Gelsenkirchen should be their live game that Saturday rather than England's search for consolation in Frankfurt.
'Guardian' chief sportswriter Peter Corrigan opened an excoriating piece on the English involvement in Euro '88 thus: "While the English were attempting to lay waste to Stuttgart, Dusseldorf, Cologne and Frankfurt, the Irish were serenading Hanover and Gelsenkirchen with laughter and song and nothing more uncouth than the odd belch - and even they were due more to the uncontrollable aftermath of German beer than to bad manners."
In interviews, the Irish players were growing bolder, more assertive.
Asked about the squad's expectations, Mick McCarthy told journalists: "It's respect that we want. People treated us like a pub team when we first came out. We've proved to be a very good pub side, haven't we?"
Every bit as good as the Holland team of superstars, Ruud Gullit, Marco van Basten and Ronald Koeman too, only to be undone by an 82nd-minute offside goal from Wim Kieft, the ball spinning agonisingly out of Bonner's reach.
Ireland might easily have drawn, Paul McGrath watching his header rebound to safety from a post.
So the Dutch goal, an outrageous fluke, was enough to bring an end to Ireland's first appearance at a major football tournament.
Afterwards Dutch captain Gullit led his players down to the Irish end of the stadium to applaud the supporters in green. One week later, he and Van Basten would score the final goals in Munich (the latter's a never-to-be-forgotten volley) to beat the Soviets 2-0.
An estimated 250,000 people lined the streets of Dublin to welcome Charlton and his players home, the group flying into Dublin airport in an Aer Lingus jet renamed 'Saint Jack' for the day with a message reading 'Ireland You Are Magic' emblazoned across the door.
It would take 40 minutes for the open-top bus to snake its way from Parnell Square, down O'Connell Street and back again to the Civic Gallery, the Taoiseach declaring Charlton "an honorary Irishman".
And the main front-page headline in the following morning's Irish Independent read: 'Mobbed by the Nation - Jack and his Heroes', next to images of a homecoming that could scarcely have been more spectacular had they brought the Cup itself back.
Had it all been a dream?
"I think we'd have won the Championship if we had beaten the Dutch!" declared FAI president Fran Fields afterwards rather boldly.
Life itself hadn't exactly changed in our mixed-up little country. But the way we saw our football team would never be the same.