I think actual stats are more for a guide for drafting, then actual following true to form.

The point is, it's all a formula.  If a guy had one passed ball all year in RL, that severely decreases the chance he'll have one in a SIM game...but it can still happen.  And then if he gets one, the chances of another one are still the same in each game after that...they don't decrease even more since he's matched his RL total.

I'll bet some seasons of that Pudge don't have any passed balls.  It all depends how the cards come down.

Ivan Rodriguez ended the SIM season with 10 passed balls.  Your explanation might be valid if he had 1 or 2, or even 3 PB, but it can't be reasonable to have 10 PB based on actual statistics if he had only 1 PB in real life.  The probability that 1 in a season would hit 10 times...! 

And, using your logic, 1975 Johnny Bench, who had 0 RL passed balls, would have 0 PB in a SIM season,  After 61 games in a current SIM season, Bench has 5 PB already.

[Both of these catchers are at 100% in every game, so fatigue is not a factor here.]

Don't players who have a 1.000 fielding percentage in real life actually make 0 errors in the SIM if they are always at 100% and not out of position?

I think that passed balls must be a purely randomly generated number, with the range of hits possibly modified by the catchers' ratings, and it is not based on the real life number of passed balls in any way.  [I could be wrong, though.]