How do crocodiles stay fit?
Let us start with difference between humans and crocodiles. There are lot of differences but the one which matters in current discussion is thermophysiology. 

Unlike humans, crocodiles are cold blooded animals (more specifically ectotherms). These animals needs to get heat from environmental sources to maintain their body temperature. As contrast to humans who can get heat from internal metabolism. That is the precise reason crocodiles are seen always not moving and basking in sun light when it is cold (while go to shade or water if it is hot). Read this for more elaborate strategies they use. If you want scientific reference, you can check this, this or this. 

On your exercise point, there are few reports which suggest exercise can enhances aerobic capacity in young crocodiles. In this study they actually put crocodiles on treadmill and checked affect on their respiration. This report suggest  crocodile uses 3 different kinds of muscle mechanisms for lung ventilation. These three act differently in different conditions (means one acts during rest while other during high metabolism). However I couldn't find any information regarding atrophy. 


  how can crocodiles remain so fit if they don't do any exercise? What distinguishes animals that need to exercise to be strong from animals that don't? 


Short answer: Their body metabolism. 

Their body metabolism is different from human's. Although doing exercise  might help in their aerobic capacity as mentioned in reference above.