In some companies, safety training programs are merely "check-off–the-box" exercises for compliance purposes. Companies with these low-information programs predictably have major "accidents." In other companies, the management is dedicated to promoting a safety culture. This is the kind of company you want to work for or help change your company into if it's not there yet.
Nevertheless, even extensive safety training doesn't make anybody any safer. A safe workplace exists only when you and your coworkers use what you learn. It's not the training that makes you safe, but how you apply the training.
Attitude is the key to staying safe. Rather than look at safety as something that interferes with your work, look at it as your guiding principle for every task you do. Think of safety as how you work, rather than a hindrance to your work. Bonus: Safe work practices, due to their methodology, can provide a net increase of efficiency.