Warren and Mike each discuss the idea of NFL players staging a sympathy strike in  solidarity with the NFL referees' union, with player safety as the  purported hook. This also has been a recurring theme in media criticisms  of the NFL--that the league, despite its purported concerns for  concussions and player safety, is jeopardizing player safety by using  replacement refs of questionable ability, and all over a relatively  small-value labor dispute. Mike's e-mailer captures it when he insists that the NFL has an argument "the minute an NFL player is injured because of a bad call."  
But this arguments suffers from serious causation  problems. How exactly does a bad call "cause" the injury in any legal, or even logical, way? I do not see how using unskilled replacement refs creates a greater risk  of injury or how replacement refs will cause more injuries with their  terrible calls and non-calls. The likelihood of an incorrect call or  non-call on a given play does not affect the likelihood of  an injury occurring on that play. In other words, whether a penalty is called (correctly or incorrectly) after a play is over does not  affect whether an injury occurs on the play itself. If DB A hits Receiver X coming across the middle, Receiver X may or may not be hurt on the play,  whether or not a penalty is called on the play and whether or not a penalty should have been called; if DE B hits QB Y,  QB Y may or may not be hurt, whether or not a penalty is called or should have been called. In no sense did the incorrect call or non-call "cause" the injuries on those plays.
Plus, even with the regular refs, injuries regularly  occurred on plays in which no penalty was called, with the league  coming in and imposing fines after the fact for certain conduct. Also, most "bad calls" that refs are going to make or not make it are unconnected to injury; that missed Offsides is not going to increase anyone's risk of injury. So, at best, we are talking about a small subset of calls and plays. And, of course, lots of injuries occur on plays in which no penalty  should be called because no one did anything against the rules; they  just played an inherently risky game.
The  only conceivable argument is that the replacement refs will have less control of  the game and will less accurately call certain dangerous conduct (late hits, hits to the head, hits on defenseless receivers), causing players to try to get away with more knowing that they  will not be caught or penalized, resulting in more injuries. Several problems with this. First, it is necessarily cumulative; it will not allow for proof that one injury was caused by the refs, but only proof that a series of bad calls incentivized a given play on which an injury occurred. That is a tricky logical chain to navigate. Second, it is impossible to show that DB A wouldn't have gone high on the receiver even if he knew there was a greater chance of being penalized. So, again, we have the problem of a causal link between some bad call(s) and the injury itself.
Third, and most importantly, the argument assumes the  replacement refs' awfulness will run in the direction of being more lax  and giving players more incentive to engage in dangerous or  injury-threatening play. But it may be just as likely that the refs will  err on the side of over-calling penalties, imposing a disincentive on players as to how they play. If the replacements improperly call lots of  unwarranted penalties on hits to the QB, defensive players are going to ease up on  anything close, not wanting to risk a penalty. The result is bad  football because the refs are just getting things wrong and because  defenders are losing the opportunity to make plays. But the result is  not a reduction in player safety--in fact, player safety would seem to  increase, as QBs are going to take fewer hits.
At some level, player safety has become an unfortunate talisman for the players and for the media to trot out over everything. And there are lots of reasons  not to want the NFL to allow less-skilled officials onto the field. But  the leap to connect bad officiating to player safety is a long one that is not  obviously warranted, at least not ex ante.