Level of perceived disability is linked with fear-avoidance behavior (FAB). FAB refers to the fact that the person is afraid it's going to hurt, so first they slow down. Eventually they may even stop moving in one or more direction. They change the way they move to avoid pain but also because they are afraid it will hurt.
As you have suggested, cecreased activity is the first step toward increased stiffness, loss of flexibility, and more pain for those who already have pain. Increasing physical activity and exercise is highly recommended, both for this age group and also for this problem.
Take stock of your community resources. For example, is there a walking group at the mall your father could join? Many older adults find this a good way to increase activity safely. They can walk as far as it's comfortable and sit down to rest as often as needed.
What about a membership in a health club? Many older adults get a lot of help by being with other active adults. They can take advantage of the pool or hot tub. There may be yoga or fitness classes geared toward seniors. If finances are a problem, maybe the family can pitch in together and purchase a membership as a gift.
At the same time, find out if there is any medical treatment that can help. Sometimes analgesics for pain or antiinflammatories can help this condition. If he has not been seen by a physician lately, make an appointment to review the possible options for pain control.