I just took a pilates class this morning and was wondering about my lower back. I have heard this before, including the practice of yoga. I have lower back problems and after class i do feel some soreness. Instructors never ask about your medical conditions. This is probably something they should be doing.
Unfortunately, it is studies like this that will prevent many people from receiving help. I have been practicing and teaching Pilates for a quarter of century. I have found that most people have never activated the muscles that this doctor discusses. When they try to "draw in", they immediately activate their glutteal muscles, and that is what puts pressure on the lower back and threatens the well-being of the spine.
The individual who also commented is right: instructors should be asking people about pre-existing medical conditions. They should also be offering instruction on proper technique so that injuries are avoided. But to simply say that "Pilates can increase back pain" is like saying that "pharmaceuticals can make people ill". True, but only in irresponsible hands.