To my knowledge only the airlines and then only the major ones actually have a company physical exam. If you apply to a company and they fail you because they have different standards than the FAA you have recourse under the Americans with disabilities act.
Realistically if you have a 'static defect' that has been cleared by the FAA then they will have no option but to employ you.
i.e poor eyesight, poor hearing, a physical handicap , poor colour vision and many others would be considered static defects as they are not likley to get worse while you are employed.
On the other hand if they find a progressive condition then the company will be able to deny you a job on medical grounds using the argument that they are going to invest heavily in your training and will not be able to recoup their investment.
examples of progressive conditions are
Cancer, HIV, MS, Motor Neuron disease etc
American Airlines has got a captain flying for them with only one eye
Hope this helps.