''He was calm,'' Hunter said of the unexpected visitor to spring training. ''I guess he's used to being around people.''
Hunter and the Tigers are laughing their way toward opening day, approaching spring camp with a mix of relaxed lightheartedness and serious focus under new manager Brad Ausmus.
Whether it's a player posing with a reptile or a backup catcher donning a women's swimsuit next to Kate Upton, the three-time AL Central champions certainly look like they're the class of the majors when it comes to viral photos.
The Tigers also had fun under Jim Leyland, whose old-school sense of humor was always a hit. But Ausmus seems to be going out of his way to foster a sense of clubhouse camaraderie.
''At the end of the day, we're playing a game,'' Cy Young winner Max Scherzer said. ''We're playing a game for a living, and you've got to have fun in this game, because there's so much failure, inherently, within baseball.''
The Tigers have been a loose but professional bunch throughout their run of success, and Hunter was acting very much in character when he tweeted a link Tuesday to the blurry picture of him and the alligator. He said later he puckered but didn't actually kiss the animal.
The gator's arrival was apparently the result of a visit by some players to a nearby theme park.
''We had the rookies go and do a report,'' Hunter said. ''They had like a camera and microphone, and walked around and different animals - tarantulas, pythons, everything. ... We did a film and then at the end of it, they had a delivery.''
''A knock on the door, and somebody opened the door - it was a delivery for Miguel Cabrera. Miguel was about to get it, and the box started moving - like something was moving in it - and Miguel took off running.''
The alligator turned out to be relatively harmless, its mouth bound shut.
''We just had fun with it, took pictures with it,'' Hunter said.
Leyland, Detroit's manager for the last eight seasons, was known for his ability to relate to players much younger than him.
''He was having fun in his own way,'' Scherzer said. ''He can moonwalk, he can dance. The jokes he tells are so X-rated I can't even tell you. It's stuff like that.''
The 44-year-old Ausmus took over in November, with his Dartmouth pedigree and refined manner - but he clearly understands the importance of team bonding.
The alligator stunt was part of the Tigers' morning meeting, which is a new element of the team's daily routine. Lest anyone think the players are turning their spring training complex into ''Animal House'' - literally and figuratively - Ausmus says these gatherings involve more than just goofing off.
''The point of the meetings are to kind of get the team together and have some fun and build camaraderie. If it's working, then great,'' Ausmus said. ''We tend to business in those meetings as well, but we have some laughs while we're in there.''
The photo of Hunter surfaced a couple days after another Tigers-related picture began making the Internet rounds.
Reliever Joba Chamberlain's Twitter followers were treated to a shot of Detroit catcher Bryan Holaday posing in a women's swimsuit at a get-together with teammates.
Next to Holaday in the picture was a more conventionally dressed Upton. Tigers star Justin Verlander has been spotted with Upton on occasion, but he's never said much publicly about the nature of his relationship with the swimsuit model.
Holaday has played in 22 major league games. Now, he's a bit of a social media sensation.
''He did an unbelievable job,'' Chamberlain said. ''He probably could have used a spray tan before, but we'll have to work on that.''
Scherzer is in the foreground of that picture wearing a sombrero.
''We had a theme - taco night - for a cookout,'' Chamberlain said. ''We've done cookouts and stuff before, so we tried to mix it up and had a taco night.''
So the Tigers are enjoying themselves, breaking up the monotony of baseball's preseason in whatever creative ways they can think of. Players have also been participating in a basketball shooting competition, which is tracked on a big bracket posted in the clubhouse.
There's already been plenty of trash talk about that. It's all healthy fun to an experienced team that has probably earned the benefit of the doubt as far as balancing preparation with laughter.
''It's baseball,'' Scherzer said. ''If you're not smiling and having fun while you're getting better, you're not playing this game right.''