My 2 cents.
Unless the rules state otherwise, any player that is Knocked Down may be injured. The opposing coach rolls two D6 and adds their scores together in an attempt to try to beat the Knocked Down player's Armour value. If the roll succeeds, then the opposing coach is allowed to roll on the Injury table
There are cases in the rules where "may" does not imply an option and is read the same as "might." It "may" happen depending on the die rolls or previous actions, not depending on a current choice.
Examples:
the thrower may completely fumble the throw
the ball may be intercepted by an opposing player
Star Player points which may give them Improvement rolls
Journeymen may take the total players on the team . . . to more than 16
it may take you above 11 players (x2)
the current Action may be lost
A bomb may be intercepted or caught
On a roll of 4+, he may use the team re-roll as normal.
before the re-roll may be made, his coach must roll a D6.
and many more where the idea of a choice when it says "may" would make no sense
Similarly "is allowed" can be based on previous events not choice. The language does not require to be interpreted as choice, but could be in comparison to the converse. If the armor roll is failed the injury roll is not allowed.
Given that Tom (and most of the other respondents) thinks the injury roll should be required, and the rules can be interpreted that way, I know where I stand.
