It's fascinating to me to think that exercise shouldn't be priority in any injury state. If you think about it, it's really the only form of recovery that we, as human beings, are technically evolved to utilize. Cavemen didn't have massage and ultrasound. Heck, as recent as a few hundred years ago we were still putting leaches on our skin to cure fevers. At the end of the day in human history, people recovered because they continued to work their bodies and force their muscles, bones, and joints to adapt and heal. Modern-day modalities are fantastic, but they are just tools to aid the process. Movement, inherently, can do much more than these tools can.
When we have an acute injury, no matter how simple or severe, continued movement and muscle contraction is key to recovery. If you tear a muscle or ligament, immobilizing the injured area is going to lead to further complications due to allowing the muscle to atrophy and inhibiting circulation to the area. Furthermore, avoiding movement does little to discourage your body to cease its spasm response.
Always, when I see a new injury occur, whether it's an ankle sprain, should sprain, or groin tear, I initiate an early-rehab process involving basic movement of the joints. If you roll you ankle, for instance, then you should still be flexing your foot up and down (within whatever range is pain-free) to promote proper scar tissue alignment and allow blood flow to the area.
When All is Gone
But wait, you say, what if the pain is so severe that any joint movement at all is agonizing? Well, then we modify. If pain is severe, inflammation is incredible, and function is non-existent, then we still want to initiate the body's inherent healing response.
For example, if you have a massive groin tear and can barely move your leg at all, then we simply don't move it. That doesn't mean that we're not going to work it. If it takes putting a few pillows between your legs just to have you give them even the most minute squeeze with the legs to have some contraction in the injured muscle, then that's what we'll do.
And what that will do, is more than you may think. Those contractions, regardless of how small, will allow the tissue to know which direction to align its healing fibers in. The pumping of the muscle will bring circulation to the area and help move excessive fluid and swelling out. Activating those muscles will also help and minimize the amount of muscle tone that is lost while movement isn't possible, decreasing the amount of secondary complications and rehab time later on.
Hopefully you can see why delaying on exercise when an injury occurs will, certainly and absolutely, delay your recovery. By not partaking in some form of movement for rehab - no matter how big or small that movement is - you're allowing disorganised scar tissue to develop, letting the muscle atrophy and lose tone, and inhibiting blood flow and nutrients to the area. Exercise is always medicine. It always has been and always will.