Assuming his knee pain is not from another cause, running on a treadmill in moderation is reasonable. He may want to consider even lower-impact exercises such as swimming.
Exercising at other times is actually recommended. The benefits of exercise certainly outweigh the risks but must be done in moderation and sensibly. If your husband has mild knee pain following treadmill running then he may be experiencing some joint damage the gout has created over the years. Running is considered high impact and he should consider changing to a low impact activity like walking, bicycling, swimming, elliptical or stair climbing. These low impact exercises will likely provide good aerobic activity without the high impact to the joints and will help reduce exercise-induced pain and chronic damage.
Generally speaking, motion and strength far outweigh the problems of a weak knee.