Yes I agree it is speculative but the evidence (both scientific and the current epidemiology of injuries this season) would suggest we don't.
To me that would suggest those teams are implementing methods that are successfully reducing the risk of players getting injured. Mourinho is apparently very good at periodising training to minimise injury risk.
Essentially, although we don't know exactly what City do behind the scenes, the buck stops with Pellegrini.
It isn't bad luck, it is due to extraneous factors such as fatigue/poor conditioning as you mentioned. 'Soft tissue injuries' is an all encapsulating term for muscle/ligament/tendon injuries.
To me it would seem Pellegrini either a) doesn't perform the right training at the right time, b) implements a strategy that puts high loads on the players or c) doesn't allow for full recovery between matches (<3 days recovery between games does exacerbate this).
Personally I'm not dismissing anything you've said. You've clearly put a lot of intelligent thought and time into this.
However if you are to lay partial or majority of blame at Pelkegrini's door then a little more knowledge of Pellegrini's past, the players individual past and some more insider knowledge would be needed.
If we're to blame the manager, his systems and training regimes then we'd have to see what the injury record was in Spain. I doubt he did quiet so well with Villareal and Malaga with injury ravaged squads.
Can't argue that our soft tissue injury situation is in no way unlucky or a fluke.
I personally believe there's a cocktail in errors. Manager, players personal injury record, fixtures and other teams approach.
We have too many players who fit all the above.
Take Aguero.
A key player who must play. So he plays a lot when fit. He is also a target for opposition. See Palace away. He also has a poor personal injury record pre City.
We started the season with injuries, no back up full backs, very light in midfield and one senior back up striker. We then lost Aguero and Konpany. Then Silva.
This puts huge pressure on the remaining players and manager and allows very little room for rest and rotation.
As I see it, if you start with injuries its a self perpetuating cycle. We now have what? 13 fit senior pros for our busiest few weeks. More injuries are likely due to overload. Not sure there's much we can do.