Am I correct in thinking that someone who has a permanent partial disability rating due to a back injury and has a permenant restriciton limiting them to Medium/Heavy work, would qualify as having a disability under the ADA even though the doctor discharged them from care and specified the person should be able to meet the physical demands of their normal duties? 

The answer with the ADA is ALWAYS -- it depends.

The individual has to be substantially limited in one or more major life activities to qualify as "disabled" under ADA. So, to determine whether the employee is covered, the employer should determine (1) whether the employee is substantially limited in one or more major life activities (by existing or new medical certification); and if so (2) whether a reasonable accommodation exists that can help the employee to perform the essential functions of his or her job (and is not an undue hardship on the employer's operations. A reasonable accommodation does NOT require the employer to reallocate the essential functions of a job.

So, in the case where the employee is "substantially limited in one or more major life activities" and those activities do not happen to include work, the employee may not even require reasonable accommodation to perform the essential functions of his/her job.

If the employee can do their job just fine without any accommodation, then the employer does not have to worry about ADA. If thepermanent restriction on medium/heavy work impacts whther or not the employee can perform the essential functions of the job, the employer needs to look at reasonable accommodations. 

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NYGiants is right that the ADA disability analysis is whether an impairment substantially limits a major life activity.  So if the employee’s back injury substantially limits a major life activity, it's a disability under the ADA.  The reasonable accommodation analysis is related to the essential functions in the employee's job.  A person can have an ADA disability without needing an accommodation.