Bourjos said he didn't feel worthy before being convinced to go have his photo taken with "The Greatest of All Time" so he could tell his kids and grandkids all about it someday.
Torii Hunter wasn't shy at all. He was the first to jump out of his chair to go share his emotions with Muhammad Ali before his Angels would face the Giants in a Cactus League game on Wednesday.
"This guy, he's on a different level," Hunter said, eyes even more alive than usual as he watched Ali welcome Angels personnel of all stripes for photos with wife Lonnie in charge. "When he walked in this room, there's nobody else in the sports world who could make me feel that way.
"I've met a lot of famous people, but there's only one Muhammad Ali. He stands alone. I don't care who you are, no matter how big you are. Muhammad Ali comes in the room and makes you feel small, humble.
"I don't care if you're young, old, wherever you grew up. Being in the presence of Muhammad Ali is an honor."
From veterans Hunter, Vernon Wells and Bobby Abreu through the ranks of younger players such as Bourjos and Mark Trumbo, the exhilaration of the moment was visible in faces associated with children at an amusement park.
"I got to meet him the first time when I was 12 years old," said Wells, who grew up in Arlington. "He was at a card show. My dad had a painting of him standing over Sonny Liston. He signed that and a couple of boxing gloves for me, and that was a thrill.
"He's one of the special ones we'll have a chance to say we met. It's a special day for us to talk to him, be around him and his family. His presence is something few people have. His name speaks for itself."
Ali, the global icon, stretched across all borders and boundaries.
"Everyone knows Muhammad Ali, everybody in the world," said Abreu, a Venezuela native. "He fought everybody. He was fearless. It's amazing to be able to shake his hand and sit next to him like that. It's something you never forget."
Hunter has a framed photo taken of him with Ali at an earlier meeting. It is in a secure place at his home in Pine Bluff, Ark., one of his most valued possessions.
"He signed it for me with a little message," Hunter said, grinning. "He misspelled my name -- dropped an i."
The Angels' nine-time Gold Glove winner was beaming as he watched Ali leave the room.
"That's history right there," Hunter said. " 'The Greatest of All Time.' "
Lyle Spencer is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.