I think it's simply a run of bad luck. Shelton getting his ankle rolled up on, for example, has nothing to do with their training staff. Neither does Bruss tearing his ACL/MCL. Jefferson, Long, Durant? Who knows there.
And that Rams training and medical staff has been applauded here and everywhere else the past 5 years for having them be one of the healthiest teams in the league. Eventually luck runs out and things happen and we're seeing that now.
I do think that, to some extent, playing 21 games and into mid-February can have an effect on a team the following fall. They ended late. They did all go party for a while (deservedly so)... They restarted late. It can add up.