Question
Why many chiropractors don't believe sacroiliac dysfunction can be an upslip of the ilium?
Don't they teach this very important subject the same way to all chiropractors?

Some chiropractors and osteopathics tell about ilium upslip, even some books mention it, but as I go to see a chiropractor they don't seem to believe such exists. Some tell it is always only "blocked" but not shifted or slipped because there is no evidence of any abnormal positioning.

Why it is so hard to find proper information about this SIJ dysfunction? Every expert explane different theories. Some are very opposite to the others. Some tell downslip is more common. Some tell no downslip exist - it's always usplip. Some tell no slips exist - it is only rotation. Most keep telling dysfunction is pain in SIJ. Some tell pain is a result of dysfunction. Some explaine how upslip twists the spine and is responsible of the spinal problems, even in neck.

Answer
It is known that the sacroiliac joint (SI joint) can be a significant source of low back and hip pain. This has been established in the scientific literature through studies in which anaesthetic blocks have been applied to the joint, obliterating the source of local pain in the SI joint or its referred pain to the hip, groin, or lower back regions.

According to a 2005 study published in the journal Ultrasound in Medicine and Biology, while abnormal biomechanical properties of the sacroiliac joints are believed to be related to low back and pelvic pain, no objective measuring device of SI joint function is available. Traditionally clinicians such as chiropractors and physiotherapists judge the condition of the sacroiliac joints by function and provocation tests, and palpation.  

However, attempts to find agreement between multiple investigators as to SI joint mobility (or movement abnormality) based on palpation have generally been poor, as summarized in a 2008 study published in the Journal of Manipulative and Physiological Therapeutics.

Additionally, a 1997 study published in the Australian journal Chiropractic and Osteopathy found that sacroiliac joint manipulation did not statistically alter the range of motion of the hip joint.

Some chiropractic and osteopathic technique developers have postulated that manipulation of the SI joint can affect the mobility or function of other regions of the spine, but there is no evidence to show this, nor is there any radiographic evidence that the SI joint position is altered after manipulation. It is believed that perceptions about SI joint "malpositioning" on x-ray are largely due to artifact errors created by patient positioning.

Therefore, to summarize, the SI joint can be a source of low back or hip pain, and manipulation of the joint can help reduce pain in these regions, but the evidence to date suggests that manipulation of the SI joint probably has a more global effect of influencing its overall movement and neurology than in correcting a specific plane of anatomical abnormality. This will doubtless be an area of ongoing biomechanical research.

I hope that this helps to answer your question.