Contrary to idiotic reporters' beliefs, the Mariners are not replacing weight training with nonsense. As I figured, the reporter in question has no idea what "weight training" is, or rather, equates "weight training" with "leg extensions."
http://www.youtube.com/watch?v=Bsd_9zW3MyE
As you can see in the video, they have tons of cable pulleys to train hip rotation, but they also have three power cages and a DB rack. Dur hur. Dr. Marcus Elliot talks a lot about leg strength (zomg squats) and thoracic extension.
In short, they hired a bunch of non-idiots. This is likely the first case of this happening in the MLB. Or possibly even professional sports.