Ultimately yes. It is the job of the management to supply the correct equipment in full working order, maintain that full working order and to properly train all members of staff to use said equipment and to know how to report any faults. It is also the job of the management to complete risk assessments and action any necessary changes.
It is also the job of the management to ensure the welfare of their staff, to be aware of any condition that might affect the ability of each staff member to work to 100% capacity.
It`s called managing for a reason. It does not mean turning up, shutting the office door and being totally unaware of what is going on, or presuming your staff have any grain of common sense between them.
My coworker has a college education and is uneducated and he told me to do something that was against safety rules
No, even after you discount the employees who show up hung over, high, or drunk.