From the
NCAA Men's Basketball Rule Book, Rule 4, Section 15, Article 2(c):
(c) Flagrant personal fouls. Flagrant fouls are personal fouls that are deemed to be a more serious offense than a common foul. The penalty for a flagrant 1 foul is two free throws and possession of the ball for a throw-in. The penalty for a flagrant 2 foul is two free throws, possession of the ball for a throw-in, and ejection of the offending player.
1. Flagrant 1 personal foul. A flagrant 1 personal foul is a personal foul that is deemed excessive in nature (unwarranted or too much) and/or unnecessary (avoidable, uncalled for or not required by the circumstances of the play), but is not based solely on the severity of the act. Examples include, but are not limited to:
a) Causing excessive or unnecessary contact with an opponent;
b) Contact with an opponent that is not a legitimate attempt to play the ball or player;
c) Pushing or holding a player from behind to prevent a score. Depending on the severity of the contact and the potential for injury, this type of foul could rise to the level of a flagrant 2 foul;
d) Fouling a player clearly away from the ball who is not directly involved with the play, specifically designed to stop or keep the clock from starting;
e) Contact with a player making a throw-in;
f) Illegal contact caused by swinging of an elbow that is deemed excessive or unnecessary but does not rise to the level of a flagrant 2 personal foul (See Rule 4-18.7);
g) Illegal contact caused by a player hooking an opponent over or under the arm and which may lead the official to believe the contact was caused by the opponent. Depending on the nature of the contact, or the result of the contact, this foul could be considered a flagrant 2 foul; and
h) Contact with an opponent that is not the result of a normal basketball play. “Normal basketball play” is defined as any activity by a player, including incidental contact, which is generally accepted as that which occurs in a basketball game when the player is attempting to make a legal offensive or defensive play.
2. Flagrant 2 personal foul. A flagrant 2 personal foul is a personal foul that involves contact with an opponent that is not only excessive, but also severe (brutal, harsh, cruel) or extreme (dangerous, punishing), while the ball is live. In determining whether a foul has risen to the level of a flagrant 2, officials should consider the following:
a) The severity of the contact;
b) Whether a player is making a legitimate effort to block a shot. Note that a player may still be assessed a flagrant 2 foul on an attempted blocked shot when there are other factors, such as hard contact to the head or the defender winding up or emphatically following through with the contact. Depending on the nature of the contact, or the result of the contact, this foul also could be considered a flagrant 1 or common personal foul;
c) The potential for injury resulting from the contact (e.g., a blow to the head or a foul committed while the player was in a vulnerable position). Depending on the nature of the contact, or the result of the contact, the foul also could be considered a flagrant 1 or common personal foul;
d) Any contact by the offending player to the groin area of an opponent which is not clearly accidental; and
e) Any foul similar to the foul described in Rule 4-15.2.c.1.g in which the contact, or the result of the contact, is not only excessive but also severe or extreme.
Note: The above acts represent examples of potential flagrant 2 fouls. Other acts may also qualify, if they meet the criteria of being not only excessive but also severe or extreme.
I think Brock should've been assessed a flagrant 1, but a case can be made that there was a "potential for injury resulting from the contact (e.g., a blow to the head or a foul committed while the player was in a vulnerable position)." While the player was not hurt, he was pushed headfirst into a table. A concussion or neck injury were well within the range of possibilities.