Taylor's injury is not career-threatening, coach Anthony Lynn told ESPN, stating that the doctor "just made a mistake."
"It happens," Lynn said. "Tyrod's not angry, not upset."
Many coaches believe that no player should lose his job to an injury, especially one that accidentally came at the hands of a team doctor.
The Chargers previously said Taylor suffered complications from an injection.
It is rare that a player suffers a punctured lung from the injection, especially right before kickoff, sources told ESPN.
Taylor suffered two cracked ribs during the first drive of the Chargers' Week 1 win over the Cincinnati Bengals, but he played through the injury.
Doctors have advised Taylor not to play indefinitely.
"If Tyrod is 100%, he's our quarterback," Lynn said on Monday
The NFL Players Association is investigating the medical mishap according to NFLPA assistant executive director of external affairs George Atallah.
"Our medical and legal team have been in touch with Tyrod and his agent since Sunday, collecting facts," Atallah tweeted Wednesday.
"An investigation has been initiated."