When using a hair mask, you are coating your hair on something beneficial. Either you boost the moisture content or add something into your hair that it needs, like protein. Whereas when your hair is wet, it is just wet, which isn't doing really doing anything good to your hair. Also, hair masks aren't usually done every time you wash your hair. Therefore, as they are an infrequent part of your routine, they are less likely to cause damage in this way anyway.