One of the main beliefs that dictated Greek life was the practice of paying tribute to the gods, so that they would not be angry and bring down their wrath on humans, causing harm to groups or individuals.
The Greeks also had many moral and ethical values within their society, among which we can mention the obligation of men to seek political, scientific and artistic knowledge, becoming someone educated and cultured, in addition to being strong and having a warrior instinct. In addition, women should remain delicate and take care of domestic services, in addition to refraining from male affairs such as economics, politics and science.
In general, the ethical values that exist in our society also governed Greek society such as not stealing or killing, coveting what was someone else's, being obedient, among others.
if we're talking about crime and the USA, then it legally depends on what state. in most places, there's no legal obligation to report any crimes. there seems to be exceptions. if you want to cross into a moral perspective, then things get more complicated. life has a lot of other plans. maybe you are being blackmailed and can not afford to expose anything. in such situations, it may be wise to keep quiet. other times, you do not want to get involved because it is too much of a hassle. you could be regarded as a callous person for that.
however, if someone's life is in immediate danger due to a situation, i would say morals should always try take priority. you're a human being and you should be compelled to keep others out of danger. unless telling others about the dangerous situation results in negative effects applied onto yourself. you do not want to help others when you will be unable to help yourself. you are told to put your oxygen masks on a plane before helping others
if we're talking other situations such a workplace habits, keeping quiet about those may not be a legal problem. but doing so may result lawsuits, disciplinary action, and/or losing your job.