You may want to consider the limitations of physical contact during practice. When game time comes along, there is more stress during contact and a lot of that has not been addressed in practice.
It is quite possible that getting stronger in the gym increases the strain players put on their bodies and it's that extra strength, combined with physical stress in a game that exceeds what occurs in practice that is the cause for these injuries.
Like one poster stated, often the most obvious answer is the correct one. The known constants are:
1) There is reduced hard contact during practices due to NFL rules.
2) Strength training makes you stronger.
3) Players are getting bigger every year.
I do not remember any 300 pound players during the 1960's, & 70's. Some of those big guys are over 330 pounds and approaching 350 pounds. We may even be getting to the limits of how much weight and strength the human body can reliably support.
How's that for identifying an obvious cause and effect as opposed to "we have the same trainers, that must be the problem". While having the same trainers might be part of the problem, it could be because they do their job too well.