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For me, I think you can present evidence.  (I don't know what the actual numbers are, but I think one might find them).
1) How many pitchers who did NOT exceed the 30+ innings in a year limit got hurt (as a %).
2) How many pitchers who DID exceed the 30+ innings in a year limit got hurt (as a percentage).
That's a start - even if weighted to "falsely" support the inning-increase paradigm.  Why do I say "falsely?"  Because there is some basic "base rate" of chance of injury on every pitch thrown, (regardless of other factors).  That base rate we will call "unlucky" injuries, (pulling a muscle when sneezing would qualify).  Even if that luck rate is really low - (1in 10,000 chance of getting injured on any pitch), the more pitches thrown, the more total chance of getting unlucky.
Box cars on dice are a 1 in 36 chance.  While the chance on any given throw doesn't change, the odds of throwing box cars (getting injured?) in 36 rolls vs. 360 rolls is very, very different.  But, it does not matter at all whether I throw those 360 rolls all in a single day vs. over a 36-day span. 
I think James is absolutely spot on.  There are a bunch of factors that influence injury, and while "common wisdom" has fixated on innings limits, this is more likely out of a sense of "this is something we can control easily" rather than it being an actual (scientifically valid) major issue.  While pushing beyond physical endurance is a valid concern, for pitchers specifically, this seems to be a self-correcting issue.  When pitchers "tire", they get less effective and they get yanked. 
Honestly, I think a larger chunk of the whole pitch-limit and inning-limit issue is simply managers and coaches doing everything they can to absolve themselves of responsibility for injuries rather than to actually prevent them.  If industry standard says 100 pitches per game is a reasonable limit - then a manager has "permission" to yank a starter after 104 pitches, even if pitching well.  But, mostly I think it is a (bad) case of attempting to take control of something largely out of anyone's control.