But Cantu, a clinical professor of neurosurgery at Boston University Medical Center, said a thorough assessment would take "at a minimum" 10 to 15 minutes, and longer for someone whom "you're really suspicious or concerned about."
Other doctors agreed.
Bradley had stumbled to the turf after the initial contact, a moment captured by national television cameras.
The timing of Bradley's return also led a medical adviser for the NFL players' union to temper his comments defending the Eagles and instead raise questions about their evaluation.
Bradley's fall "looks like it would require a pretty good evaluation," said Thom Mayer, medical adviser for the NFL Players' Association, the players' union.
Four minutes, he said, "strikes me as very fast."
Mayer said the NFLPA was reviewing the situation. He was scheduled to talk to Eagles trainers Tuesday night.
Mayer initially said the Eagles had followed the proper concussion procedures but later revised his assessment after doing more investigating. He said that trainers did not see Bradley's fall because they were attending to Kolb, but that someone should have alerted them to the situation.
"That information apparently never got to the trainer or team physician," Mayer said. He added, "The Eagles are aware of that and are intending to make some changes."
Mayer's initial defense of the Eagles was based on information relayed by NFL medical adviser Elliot Pellman, who had spoken with the team.
Reid defended his training staff Monday, saying the team "stuck to the criteria" for evaluating players, continued to monitor them, and pulled Kolb and Bradley once it was clear they had concussions. The team was off Tuesday.
Mayer suggested that the NFL might need more stringent guidelines for proper examinations before a player suspected of having a concussion is allowed back on the field.
Many sports trainers use a Sport Concussion Assessment Tool, or a variation of it, to check for concussions. The oral exam lays out a series of cognitive, memory, and neurological tests for players suspected of having the head injury.
Kolb was sidelined for about 21 minutes before going back into the game. His college coach, Art Briles, said Kolb had never suffered a concussion before.
Much of the discussion has focused on Bradley, whose distress after his collision was obvious.
On Tuesday he wrote on his Twitter account, "Does anyone have any good remedies or a killer head ache?" (Presumably he meant "for").
Later, he wrote, "This morning my publicist tweeted about headache remedies but she didn't need to ask cuz i haven't even had a headache. Seriously."
Bradley's fall should have been all that trainers needed to see, said Douglas Smith, director of the Penn Center for Brain Injury and Repair.
"If you're really stunned and stumbling and can hardly gather yourself together, in my mind there's almost no need for one of those tests," Smith said. "It's evident what happened."
Still, Cantu and Richard Ellenbogen, cochair of the NFL's head, neck, and spine committee, both said falling over is not a definitive sign of a concussion. Both relayed a story about a player who went to the ground holding his head - after being struck in the groin.
Smith said it was "generally accepted" among doctors, though not proven, that anyone who has a concussion is at increased risk of further damage.
"All the thresholds for injury are lowered because of the first injury," he said.
On Bradley's first play back on the field, he lowered his head and shoulder into running back Brandon Jackson to help make a tackle.
Contact staff writer Jonathan Tamari at 215-854-5214 or firstname.lastname@example.org.