No one can know for sure what effect pain can have on each individual’s function and abilities. As you suggest, some people are better able than others to push through the pain. Others perceive greater disability due to pain than you might in the same circumstances.
People who say they can’t do something “because my pain won’t let me” are medically labelled as symptom magnifiers if they do so unconsciously. If this is a conscious response in order to get out of doing work, then they are referred to as malingerers.
Most people who are off work due to a work-related injury or accident are being followed by a Workers’ Compensation (WC) case manager. It might be helpful to bring your concerns up to the manager or board for consideration.
Though they can’t discuss individual clients with you, the WC manager can take your thoughts and concerns into consideration when working with your employees getting them ready to come back as soon as possible.
There are ways to test for perceived disability due to pain (e.g., the Pain Disability Index (PDI)). Other tests such as the Patient-Specific Functional Scale (PSFS) can help measure functional limitations keeping the person from resuming work duties. Once areas of limitation have been identified, then the rehab program can be geared to deal with those specific problems directly.