It should, because in 2003 the Swans beat the Tigers 4-2 to ensure survival in the Football League and start a journey that culminated in six seasons in the top flight - so far.
Fourteen years on from James Thomas' hat-trick at a decrepit Vetch Field, the two clubs are once again locking horns to avoid the drop.
This time there is a place at English football's top table at stake.
Swansea's presence in the Premier League is a testament to the magnitude of that last day win over Hull in the old Division Three.
They have not looked back. The startling rise through the divisions and 2005 move to the Liberty Stadium saw them described as a model club.
Now the Swans face their greatest challenge yet to remain among the elite.
And it's advantage Hull, who have a precious two-point advantage over the Welsh club with just five games to go.
Crystal Palace's win over 3-0 win over Arsenal on 10 April helped them open a six-point lead over the Swans.
It also followed an astonishing 2-1 victory at Chelsea nine days earlier, underlining how difficult predicting the outcome of the relegation battle is in reality.
After the Arsenal win, Palace manager Sam Allardyce pointed out: "We have beaten two of the top teams in the league in the last week. It shows anything can happen in this league. That's what's so good about it.''
Some coaches and managers insist they do not pore over league tables. Tables are for fans, they say. That's always been hard to believe.
At least Nigel Gibbs, the assistant to Swans boss Paul Clement, does not pretend that is the case.
He told BBC Radio Wales Sport: "We've all done it. We are only human. We are looking at the other teams' fixtures and what points they could possibly get.
"I would imagine it's going to be 36 or 37 points. But you just never know. It's so difficult to predict.
"All we have to make sure is we are fourth from bottom. That is the most important thing. Whatever points total that is, we will take."
Swansea City and Hull City were struggling when they appointed new managers at the start of 2017.
Paul Clement became the Swans' third boss of the campaign on 3 January when he succeeded Bob Bradley.
Bradley was the first American to manage in the Premier League but won only twice in 11 games.
Hull City moved just two days later to replace Mike Phelan with Portuguese Marco Silva.
"Marco Who?" some asked as they headed for the internet.
Silva actually arrived with a formidable track record with unfashionable Estoril, Sporting Lisbon and Olympiakos.
Both bosses had the desired effect on their teams.
Clement was actually supposed to have a watching brief in his first game as Alan Curtis took the reigns at Crystal Palace. But Clement could not resist.
He appeared on the touchline during the match as they won 2-1.
That was followed by a stunning 3-2 win at Liverpool in which Fernando Llorente and Gylfi Sigurdsson both scored, and Clement's improvement in his side's defensive organisation was plain to see.
Home wins over Southampton, Leicester City and Burnley took the Swans to the relatively comfortable height of 16th before what now seems a hugely damaging 2-1 defeat at Hull.
Momentum is everything at this stage. The Swans lost theirs at the KCom Stadium and have not won in five matches. They lost at Bournemouth and West Ham, while a home draw against seemingly doomed Middlesbrough felt like a defeat.
It continues to be home sweet home for Silva. He has inspired five wins out of six in the Premier League on Hull's own turf, continuing his remarkable managerial record of not having lost a league game at home in more than three years.
His last home defeat in league competition was for Estoril against Rio Ave on 30th March, 2014. That's 40 league games!
Whatever Hull City's fate, Silva's future seems assured having lifted the Tigers from the bottom place when he arrived, to a fighting chance of survival now.
The teams have similar run-ins to the end of the season. Swansea next face Stoke at home after their away defeat by Watford. Meanwhile Hull, who lost to Stoke on Saturday, go on to face Watford next.
Both teams have to play bottom club Sunderland, while Hull's enviable home record will be sternly tested by Tottenham on the last day.
Swansea face West Brom on the final day, after facing Everton in their penultimate home game.
Palace's daunting remaining fixture list suggests they can still take nothing for granted, though it seems more likely one of  Swansea or Hull will go down.
James Thomas, who became a paramedic after retiring from football, ensured a never-to-be-forgotten finale to that season 14 years ago.
Now the Swans need another life saver.
CRYSTAL PALACE (Seven games left) 34pts
April
23rd: Liverpool (a); 26th: TOTTENHAM (h); 29th: BURNLEY (H)
May
6th: Man City (a); 13th: HULL CITY (h); 21st: Man Utd (a)
HULL CITY (Six games left) 30pts
April
22nd: WATFORD (h); 29th: Southampton (a)
May
6th: SUNDERLAND (h); 13th: Crystal Palace (a); 21st: TOTTENHAM (H)
SWANSEA CITY (Six games left) 28pts
April
22nd: STOKE CITY (h); 30th: Man Utd (a)
May
6th: EVERTON (H); May 13th: Sunderland (a); May 21st: WEST BROM (H)
MIDDLESBROUGH (Six games left) 24pts.
April
17th ARSENAL (h); 22nd Bournemouth (a); 26th SUNDERLAND (H); 30th MAN CITY (h)
May
8 Chelsea (a); 13th SOUTHAMPTON (h); 21st Liverpool (a)
SUNDERLAND (Seven games left) 20pts
April
26th Middlesbrough (a); 29th BOURNEMOUTH (h)
May
6th Hull (a); 13th SWANSEA CITY (h); 21st Chelsea (a); TBC: Arsenal (a)
Swansea City against Hull City in a battle for survival in the Premier League - does that have a familiar ring to it?