"Massage can help increase a joint's range of motion"
This statement almost seems impossible. Massage works on the muscles and soft tissue, not bones and isn't a joint a bone? Yes, a joint is made of where bones meet to allow movement, however bones don't move by themselves. They are surrounded by ligaments, tendons, and muscles that allow them to move. When someone has an injury to a joint, there can be bone-related injury such as a break or a dislocation, but most of the time a simple or chronic joint injury is more an injury to the muscles, tendons, or ligaments that make the joint work. Unfortunately, like a break or dislocation, repairing a muscle, etc injury isn't as easy as "pop it back in and leave it immobile to heal". While keeping the joint immobile can speed healing in that it isn't being moved and getting re-injured or irritated, when muscles don't move for an extended period of time, they can start to atrophy or get tighter and stiffer. Likewise if the injury involves any type of tearing or even surgical repair, scar tissue can build up and scar tissue doesn't stretch well. So if everything surrounding the joint is getting stiffer and harder, the joint isn't going to be able to move as far or as easily since everything around it has tightened up. The usual amount a joint can move is what we refer to as "range of motion", or ROM. Range of motion is one thing doctors and therapists use to determine how well or quickly something has healed, and one of the goals of healing from an injury is to get back to the previous range of motion so the joint can fully do what it's supposed to do.
Massage helps by working on all of these muscles, ligaments, and tendons that surround the joints and breaking up the scar tissue, re-introducing circulation, and softening up the muscle fibers that will then allow everything to work again and will stretch and contract the way they should to help the joint do what it needs to do fully. Like everything, it is often not a one-time fix. Depending on how long the injury has been there, and how severe it was can change the amount of time and how many sessions it may take to make a noticeable difference. Sometimes a small amount of ROM can be improved immediately, but like all types of healing or rehabilitation, you never want to go too far too fast or else the risk of re-injury is possible. Nonetheless, massage can be a valuable asset to helping joints reach their maximum capacity.
Also, it isn't just for healing or rehab. If someone is training to build strength or increase flexibility for sports or any type of physical activity or endurance, massage can additionally help in conjunction with stretching and the training to increase the ROM of the joints and therefore make the training more complete. Adding massage to training may also help reduce DOMS and training-related injuries and setbacks, keeping everything healthier and therefore working better.