I'm a doctor. Grading and treating concussions is highly variable from sport to sport, different age groups, and between doctors. My thoughts are these:
1) If Urban Meyer really said that Tebow's injury was "no big deal" then he's a fool. Even if Tebow never lost consciousness and was 100% alert/oriented with no memory loss with 30 seconds of the impact, concussions are never a "no big deal" kind of injury.
2) Based on teammates comments about "eyes rolling into the back of the head" I think its likely Tebow was unconscious briefly. Based on the film I've seen, its probably just a couple of minutes at max. Whether he was knocked out or not is important, because it changes the grading/evaluation and recommendations for concussion management.
3) In terms of the management of the field team, I'm assuming that team includes a sports medicine doctor (usually an orthopedic surgeon) and several athletic trainers. Not all concussions require monitoring in the ER or an overnight hospitalization. I'm sure they quizzed him about any neck pain or numbness/tingling/paralysis in his extremities and checked his cervical spine for point tenderness. I'm assuming he passed all phases of that exam, and in that case it is not necessary to immobilize Tebow in a c-collar. On the other hand, if he was unable to respond or wasnt visibly moving extremities upon command, then yes they should have placed the collar on him and immediately transported to the hospital. I'm assuming that once they got him to the sideline, they did a thorough cranial/scalp exam to assess for any point tenderness, swelling/bruising and didnt find any, making a skull fracture unlikely. Assuming they did all those things that I listed above, then I cant find any fault with how they dealt with him. At the point he started vomiting, they made the appropriate decision and took him to the hospital. Medical status changes constantly, and just because he ended up at the hospital later does NOT mean that the doctors/trainers made an error in not sending him sooner.
4) To really get a full assessment of the severity and management recommendations for anybody, its critically important to know about their concussion history. If you have 2 people who get a grade I concussion (minor) and one of them has never had a concussion before while the other guy has had 3 prior incidences of concussions including one requiring an intubation and ICU stay, it makes the difference between clearing the player to play next week vs never allowing him to play contact sports again. The coaches and medical staff should absolutely be able to recite any given player's concussion history. Its possible the medical staff is just not releasing the info since it could be considered "protected" information under HIPPA (federal privacy laws).
5) There are several different grading and management systems for concussions. The big 3 that are the most widely used are the American Academy of Neurology, Colorado Medical Society, and a set of evidence-based guidelines put out by a research group of neurosurgeons at Harvard Brigham/Womens Hospital led by Dr Cantu. You can google those, they are available at a bunch of websites. My understanding is that the NCAA advises its collegiate medical teams to use the Colorado Medical Society guidelines, but I cant be sure about that. The Cantu guidelines are generally the strictest/most conservative whereas the AAN guidelines allow a sooner return to play.
6) All concussions, by definition, have either amnesia to varying degrees and/or confusion. The news articles state that Tebow had passed all of his neuro status screens by 12 hours after the injury. With the vomiting and the loss of consciousness, thats automatically at least a grade 2, no matter what system you go by. According to the CMS and AAN guidelines, its already grade 3 injury.
7) Assuming that this is Tebow's first concussion of the season, then here are the recs:
Cantu: out for 1 week
CMS: out for 1 month (assuming + LOC of any duration)
AAN: out for 1-2 weeks (assuming + LOC and depending if LOC is seconds or minutes long)
8) If this is Tebow's 2nd concussion of the season, then the management recs become MUCH more stringent/conservative:
Cantu: out for 1 month
CMS: out for the year
AAN: out for the year
As you can see, this makes a huge difference in how long the athlete is out. Urban Meyer's comments imply to me that he has not had an earlier concussion this season, because if he had, there's no chance he'll play at LSU, regardless of how well he feels right now.