During a salmon run, bears will only eat the skin and discard the rest of the fish. This is because the layer just below the skin is the fattiest. Salmon skin isn't like chicken skin, it contains lots of good fat, omega 3 fatty acids. So, yes it is healthy to eat. Bears, wolves, eagles, seagulls ( when the salmon are young ), orcas, and other fish. Also humans eat a lot of salmon.
One fascinating new area of health benefits involves the protein and amino acid content of salmon. Several recent studies have found that salmon contains small bioactive protein molecules (called bioactive peptides) that may provide special support for joint cartilage, insulin effectiveness, and control of inflammation in the digestive tract.
Since increased blood triglyceride levels can be a risk factor for cardiovascular problems, and since dietary salmon did not produce a similar rise in blood triglycerides for participants in this study, dietary intake of salmon appears to be a best bet for supporting cell function and simultaneously avoiding some unwanted increases in other blood fats.
Intake of fish rich in omega-3 fat (including salmon) is associated with decreased risk of numerous cardiovascular problems, including: heart attack, stroke, heart arrhythmia, high blood pressure, and high triglycerides in the blood.