Someday, they may appreciate the story line a little more. When the puck has thawed and the crowd has dispersed, they may recognize the compliment in the insult.
But for now, it is the rejection that drives them. The trade, the benching, the demotion. The release, the slight, the slur.
You want to know how a team survives the opening round of the playoffs after losing three of its first four games? Ask the guy who was traded five times in four years and left three other teams via waivers or free agency.
You want to know how a team falls behind 3-0 against one of the best defenses in the NHL and then comes back to win? Ask the goaltender who saved the day just three months after being snubbed by every GM in the NHL.
You want to know how a team goes from three consecutive losing seasons and three successive ownership groups to the cusp of the Stanley Cup final? Ask the head coach whose NHL resume was still completely blank by his 40th birthday.
It is not in spite of its setbacks that Tampa Bay is winning.
Rather, it is because of them.
"I don't think it's a stretch at all to say that," Lightning coach Guy Boucher said in a hallway of the TD Garden on Sunday afternoon. "This is the type of team we've got.
"We have a lot of guys who needed to prove some things. Guys who have had setbacks in their career. Guys with moments or circumstances to overcome. They were given a shot this year, and together, it's one of the things they all have in common."
Go down the roster of every team in the NHL and you will find similar stories of perseverance. So no, these woebegone tales do not make the Lightning unique.
What is curious is the way Lightning players wear their failures. The way they have almost turned their collective disappointments into a battle cry.
Marty St. Louis is wealthy, famous and quite possibly skating toward a spot in the Hall of Fame, and yet there is still a part of him that burns at the memory of being snubbed 14 years ago in the draft and being cut loose as a young player in Calgary.
Dominic Moore was traded five times before his 30th birthday. Nate Thompson was waived by the Bruins and the Islanders in the past three years. Steve Downie was regularly suspended and condemned for his brutish play in Philadelphia and the minors.
Sean Bergenheim was so unappreciated after five years with the Islanders, Tampa Bay signed him to a one-year deal for about one-third of the league's average salary.
"There are a lot of guys on this team who have been through a lot in their careers. It definitely grows character," said goaltender Mike Smith, who was sent to the minors after passing untouched through waivers then called up after again passing untouched. "This time of the year, character guys are the ones who find a way to win hockey games.
"You look around this room. There are a lot of guys who will do anything to win."
They fit well together, this ramshackle franchise and its misfit players. Rarely called among the league's elite and yet never satisfied with waiting their turn.
You see, some franchises are historic. And some markets are privileged. Tampa Bay is neither. The Lightning has bounced from owner to owner and arena to arena while trying to hold on to fans in a community that is neither wealthy nor rooted.
So is it any wonder the franchise has attracted a fair number of players with similar tales of being forgotten, ignored or overlooked?
"On TV, they talked about all the rejects we had. Like half of the team was a bunch of rejects," Boucher said. "You hear that, it makes you feel you have to prove something.
"I like those kind of players. Oh yes, I like them."
In Boucher's mind, the NHL focuses too much on what players cannot do. The Lightning, instead, is trying to figure out what it can do.
Embrace a specialty. A trademark. A role. Teach a player to stay within a particular type of game and celebrate all of the little moments that go unnoticed.
In the meantime, do not be surprised if Boucher continues to tap into their insecurities. If he occasionally reminds them of who they are not.
For every Vinny Lecavalier on this roster, there is a Nate Thompson. For every Victor Hedman and Steven Stamkos, there is a Mike Lundin and a Dominic Moore.
Players who have never been celebrated in their careers but who have found homes, and roles and, sometimes, even glory in Tampa Bay.
"Sometimes, we think people get one shot at the end," Boucher said. "The great stories are about guys who get two, three, four shots. And they persist and persist and persist."
They may chafe today at the idea of being rejects or misfits, but the depiction grows more impressive and meaningful as they climb higher and higher.