Players, coaches and team officials try to deny it, but that does not make it less true. There are still enough memories of the club's greatest achievement - the time they kept bouncing back from the brink of disaster and reached a European semi-final - to make sure it cannot be different.
So the spotlight on tomorrow's match against Gloucester at Murrayfield is brighter than ever, and though Alan Solomons, now into his fourth month as head coach, would love to see the team playing with a level of consistency that means they can approach it as just another game, he must know the reality is different.
He saw that in October when the competition kicked off with Munster arriving at Murrayfield as the strongest of strong favourites. More than 7,000 turned up to watch and his players stunned the Irish with a performance that few had seen coming. All coaches are after consistency, though. That is why Solomons is anxious to play down the idea of any special focus this game.
"The club has struggled over a number of years," he said. "They had one run in the Heineken Cup which was fantastic, full marks to all concerned, but you have got to judge the Heineken Cup in the context that it is six games and then a play-off.
"There is no doubt that Edinburgh have gone off track in the last few years and the task that we are faced with at the moment is rebuilding Edinburgh. The Heineken Cup needs to be seen in that perspective and in that context."
And yet he also knows that by the form book Edinburgh should have little to fear. Gloucester have lost five on the trot in all serious competitions since the end of September. Their only win since September - outwith the LV+ cup - is over Perpignan in the opening European round, the same weekend as the Scots were beating Munster. The difference is that Edinburgh have gone on to win all their home games including the confidence booster of a try bonus point over Connacht last time out.
The form book, though, is not always reliable. Edinburgh's wins have come against the three bottom teams in their league and they got a hammering when they went to Belfast, while Gloucester have been facing teams in the top half of theirs and though wins have been elusive, the matches have all been tight: twice lost by two points, once by eight and once by five.
Which is why Solomons was being cautious as he reflected on his team's last match. "It was a good result but you have got to keep that in perspective," he said. "Gloucester are a more star-studded team.While they have had a tough time in the Premiership, this is a club with an enormous tradition. They have some very, very good players at their disposal and have a strong side out. They are looking at this game to put their season back on track, so it is a massive challenge, but one we welcome."
It is a message that has got through to the players. "They are a quality side, you can't get away from that," said lock Grant Gilchrist. "It is going to be a massive game and massive challenge. They play a high tempo game, move the ball a lot, pass it lot, and try to skin you. If we don't get our defence right, then it is going to be a long tough afternoon."
There is excitement around, though, and that should be enough to raise Edinburgh's performance.