Lats are stiffer than the lumbar spine
I see this all of the time when I take new clients through assessments. Someone flexes their shoulder (raises their arm overhead) and their low back extends (most likely hyperextends) rather than their shoulder reaching through to its end range. Since their lumbar spine is more flexible than their lat, this compensation occurs. Chances are, if we can get their trunk muscles to stabilize their lumbar spine and get the stiffness in the low back up to par with the stiffness in the lats, the range of motion in shoulder flexion will improve. It could also be a situation where you may need to decrease some of the stiffness in the lats AND increase the stiffness in the lumbar spine. This is a great example of why assessments are so important.
Rectus Femoris is stiffer than the abdominals and supporting structures of the lumbar spine
In this situation, the rectus femoris (big quad muscle that crosses the hip and knee) is stiffer than the supporting trunk muscles. When the knee is flexed, there will be excessive anterior tilt of the pelvis and the low back will extend. At the same time, the knee will not flex to its ideal range. In this situation, if we increase the ability of the trunk muscles to stabilize and stiffen, we might get better range of motion in knee flexion and less pelvic tilt and lumbar extension. In another light, it could be a situation that rectus is so stiff, that the body has to compensate by extending the low back and tilting the pelvis when the knee is flexed. There are various implications that could be present and Sahrmann gets into great detail on them all. But hopefully, this gives you a decent idea of what I am talking about. In my experience, it is most often a combination of stiffness in the talked about muscle and lack of stiffness/weakness in the supporting muscles. Both would be addressed to make the situation better. Again, everyone has specific things going on so not every condition will be taken care of in the same way.
A good real time example would be with the squat. Someone with an overly stiff rectus femoris in comparison to their low back will generally stand with their pelvis tilted forward and their low back extended past neutral. With this stiffness imbalance, there will be compensations within their squat pattern. As they descend into a squat, they will get to a certain depth and when their hips run out of room to move, they will move where their relative flexibility allows them to, which in this case is their low back. With someone like this, in most cases, the rectus will need some lengthening and their abdominals (usually the external obliques) will need some strengthening. The glutes and hamstrings usually will need some work as well. When you increase the ability of the muscles that posteriorly tilt the pelvis (abdominals, glutes, hamstrings, etc.) and improve the length in the muscles that anteriorly tilt the pelvis (in this case rectus femoris), the relative flexibility will be better and the squat will be a lot prettier with a stable trunk and mobile, nice moving hips.
As I said earlier, it could be a condition where all you need to do is stretch rectus and your fine. Could also be a condition where all you need to do is stiffen up the lumbar spine and your good. From my experience, it is often some form of combination. Whichever way it is, taking care of problems with relative flexibility can relieve a multitude of back, knee and shoulder pain and problems.
Hamstrings stiffer than the low back
Here is one more good example. If you lay on your back and raise your leg straight up, how high can you go without your low back flattening into the ground? If your hamstring is stiffer than your low back, your back will try to compensate by flattening in order to gain more movement. A little trick to get your leg higher is to brace your abdominals as if someone is going to punch you in your stomach. The added stability for your lumbar spine will allow your leg to raise farther without loss of a neutral spine. This example is tricky though because if it is truly hip flexor muscles that are stiff, the pelvis may be anteriorly tilted to start; thus, giving the illusion of the hamstrings being the issue when in reality it is the hip flexors that are the issue. See my past write up on misconceptions about hamstring stiffness to read more on this. Either way, bracing the abdominals will help your cause with the leg raise. Being sure that the pelvis is in a neutral position to start can clear things up.
Notice how all of these examples feature an issue with the lumbar spine being unstable and too mobile? Stability and the ability to stiffen when needed needs to be developed around the abdominal wall and lumbar spine. The inability to do this is one of the biggest and most repeated causes of back issues, knee issues and performance detriments that you will find. Yet, tons of people continue to promote more movement here with blind stretches and exercises. I've touched on this multiple times as have some of the best strength coaches, therapists and specialists in the world. Rationalize what you do. If you really do need more movement here, than by all means you better work on it. In my experience, this is a rare case.
Randomly and blindly training for flexibility does many people more harm than good. If you took the person from either of the last two example and stretched his low back and trunk muscles, his problem would become worse. Both strength training and flexibility training need to be individualized and specific. Relative flexibility is a great and proven concept. Contrary to conventional wisdom, sometimes stretching might not even be needed to improve flexibility at a certain joint. Simply balancing out the relative flexibility by increasing the stiffness at a supporting or neighboring joint will take care of the movement at the area in question. Think about how this could revolutionize what you do in the gym or in your sport. Pretty powerful stuff!