To what extent does the prime contractor verify whether subcontractors have completed safety training?

Hello, I work in safety and health at a manufacturing workplace.
We are checking whether subcontractor employees have completed safety training before entering the site.
Currently, we are only receiving and verifying the list of training completers and signature sheets sent by the company.
However, during the internal review, the prime contractor suggested that we should also verify training materials, training hours, and instructor information, so it is unclear where to draw the line in setting the standards.
Even if the training was conducted by the subcontractor itself, is the prime contractor supposed to verify each individual's completion status one by one?
Or I am wondering if it is sufficient to simply obtain proof that the company conducted the training.
Especially since there are multiple companies, it is realistically not easy to check all the data every time.
I am curious to know what kind of materials other companies collect regarding partner company training.
Do you have separate standards for new hires and for regular checks?