Groeschner, who stayed with Martinez for part of Friday, was asked if the 26-year-old was out of danger.
"I think when he's out of the hospital, he will be," Groeschner said. "He's doing fine. He wants to get out right now. He wanted to come to San Diego with me. But I don't think you can ever be too cautious."
Groeschner said that a timetable for Martinez's return to pitching won't be determined until he leaves the hospital. Giants manager Bruce Bochy took an upbeat view.
"I can't tell you how long it'll be before he's back on the mound, but I would be surprised if he wasn't pitching in a month," Bochy said.
Had Cameron's scorcher hit Martinez squarely in the eye or face, returning to pitching might not even be within the realm of possibility for him.
"You're never lucky to get hit in the head with a ball, but it could have been worse," Groeschner said.
The Giants knew that, explaining the collective, figurative sigh of relief they heaved in the clubhouse.
"It's a blessing to know that he's going to be fine," said first baseman Travis Ishikawa, who sent a prayer letter to friends in the Bay Area shortly after Martinez's injury.
Miller actually was watching MLB Network's telecast of the game in Fresno's clubhouse with his teammates, most of whom know Martinez personally.
"Everybody got quiet," Miller said. "It was a scary moment for everybody."
Such misfortune befalling any player would shock teammates. In Martinez's case, his pleasant nature might have prompted even more concern than usual. Miller summarized the Giants' universal opinion of Martinez: "'He's so nice.' That's the best way to describe him. He's a great guy. It's good to hear that he's feeling better."
To prevent Martinez from feeling leery about the possibility of another mishap once he returns to the mound, Bochy said that he might ask Padres right-hander Chris Young to counsel the rookie. Young was sidelined for more than two months last season with a broken nose after St. Louis' Albert Pujols hit him with a line drive.
Bochy added that this chat might not be necessary.
"He's a competitor. He's a tough kid," Bochy said of Martinez. "After he went down, he went back up. He looked like he was looking for the ball."