Strength does not equal stability. I have seen some really big and strong athletes who are completely unstable in positions needed for normal daily activities. Think about some activities that require stability and balance, like riding a bike. Do you have to be strong to do that? No! Four year old children can learn to ride a bike pretty easily. They just have to develop the coordination needed to perform that action first.
One thing that I have noticed is that patients have been given a lot of abdominal strength exercises and lumbar strength exercises, but nothing that facilitates the co-contraction patterns that are needed to truly be stable in functional positions such as sitting and standing. This is the missing element in a great deal of lumbar rehab protocols. I see no point in performing strength exercises for lower back pain until unstable muscle patterns are corrected. Otherwise you would just be reinforcing these unstable patterns, making it more difficult later on to address.
In my practice, I see many patients who have had disc problems for extended periods of time who have had multiple episodes. I utilize chiropractic care, spinal decompression , and functional rehabilitation designed to address the instability patterns that develop in response to pain. Strengthening comes after instability is addressed. The great thing about this approach is that stability exercises are less strenuous and can be started earlier in care when they can not tolerate strength exercises. This approach is "phase of care friendly" for that reason and the progression from stability to strength becomes a logical process that progresses as the patient's pain level decreases. This helps to prevent future episodes from happening over and over due to bad muscle patterns that, if left untreated, continue to cause pain and interfere with normal function.