It was reported, for example, that the 26-year-old from Surrey separated Vinnie Jones and Mick Harford when Wimbledon's hard men tangled during the FA Cup replay against Manchester United. "I was actually fishing the ball from the net because we thought Peter Schmeichel had scored," he says. "In any case, you'd have to be a madman to come between those two."
Another story, following Sullivan's selection by Scotland on the strength of a Scottish grandparent, had him leaping up to scream "You beauty!" when David Seaman saved Gary McAllister's penalty at Wembley. "Not true either," Sullivan chuckles. "Seaman's my hero and I was admiring the great goalkeeping as much as anything."
Some good judges, among them Alex Ferguson, are saying much the same of Sullivan. In a season when Wimbledon's challenge to the moneyed elite has been like a gale of fresh air, he embodies their success better than most. An overnight sensation to the world outside south London, he has been tied to his local club since the age of 11, having previously supported them in the Southern League at Plough Lane.
Yet in the opening week of the season, Sullivan personified Wimbledon for negative reasons. First, he was outrageously lobbed by United's David Beckham from 60 yards. David Batty then caught him doubling as keeper and sweeper to score at Newcastle. After Lee Sharpe powered another long- range shot past him at Leeds, he wondered if there was a vendetta against him and the Dons had neither a point nor a goal.
They promptly embarked on a pursuit of all three domestic prizes and go into tonight's Coca-Cola Cup semi-final first leg at Leicester with only three more defeats in 31 games. Sullivan, however, attributes his elevated profile as much to the endless television replays of his first- day disaster as to his role in the revival.
"In a funny way the Beckham goal has been the making of me. I shot to fame because of it. Suddenly everyone knew my name! People were watching me to see what would happen next and I kept four or five clean sheets on the trot."
In bizarre, archetypally Wimbledon fashion, being embarrassed by Beckham also opened up the prospect of playing in the World Cup. Alongside a feature about the goal, FourFourTwo magazine ran an interview in which Sullivan referred light-heartedly to his eligibility for the Scots. Within hours of reading it, this correspondent happened to see Scotland's manager, Craig Brown, who expressed surprise and interest.
Last week, sure enough, Sullivan was in Monte Carlo with his new compatriots as third-choice keeper against Estonia. Not everyone was pleased. "Some of the Scottish media reckoned they didn't want an Englishman playing for them, but if you heard my grandad speak you couldn't doubt my ancestry. I should be judged on my ability and commitment, not my accent.
"One journalist said he'd rather Scotland played with no keeper than a cockney. Well, Andy Goram was born in England too, and if they don't like it they should campaign for the rule to be changed, not have a pop at me. Anyway, you'd have to listen very hard to hear Bow Bells from Malden."
On Goram's debut, the crowd sang: "You're not English any more!" In Monaco, kilted fans offered Sullivan no hostility, only handshakes. They knew he was a Scottish keeper, one quipped, the moment that goal sailed over him from the half-way line.
Wimbledon are, of course, the kings of impractical joking; ties shredded, tyres let down. Some rival managers see the image as a smokescreen to obscure the quality of Joe Kinnear's squad. Not so, says Sullivan.
"It really is as mad as it sounds," he says, "though we never sit down and think: `What can we do today so that the press think we're the Crazy Gang?' The reason it has kept going through the years is that there's a hard core of lads who've been at the club since they were kids."
While that also explains a certain continuity in playing style, Sullivan insists the days when Wimbledon's keeper was their playmaker are gone. "We still like to get the ball upfield fast, but it's a lot more subtle than smashing it down the middle and hoping for a knock-down. If you'd seen my kicking, you wouldn't say that. It needs a bit of work."
Remarkably for one still some way short of 100 first-team games, after understudying Dave Beasant and Hans Segers, he shares with Dean Blackwell the longest unbroken service. Having watched the FA Cup triumph of 1988 as an apprentice, he was on the bench for the Charity Shield but has never played at Wembley.
Now he could be appearing there twice in two months. A stunning save from Gary Pallister helped break United's grip on the FA Cup, after which Sullivan had an unexpected visitor in the dressing-room. "I looked up to see Alex Ferguson coming towards me and wondered what was going on. He shook my hand and wished me well with Scotland, which was very gratifying after United's previous visit to Selhurst."
And Wimbledon are favourites to win the Coca-Cola Cup, unaccustomed status which Sullivan is sure will not go to their heads. "Leicester beat us in a tight game there a month ago. To be honest, the goal came when I came flapping for a corner and got bundled out of it. They showed the Wimbledon spirit the way they came back against Chelsea on Sunday, so they're going to be very confident."
But if the future holds any unwelcome surprises for Sullivan, Wimbledon's crazies are just as likely to be responsible. He awaits with trepidation their reaction to his tartanisation, a nickname being the least he expects to get away with. "It'll probably be Jock," he muses. "If I'm very lucky."