I was recently talking with a student who described a patient who could not load the joint comfortably. Additionally, the patient had severe wear, an uneven occlusal plane, broken crowns, and despite deprogramming with a cotton roll, he would feel quite a bit of tenderness when the TMJs were load tested.
When you're checking long centric, it's a postural closure, a very gentle closure from postural position where the jaw might posture slightly forward out of centric relation.
Load testing is an important part of verifying centric relation. The purpose is to verify that your patient is in centric after you think they are there. In order to master this technique, it takes a solid understanding of how the masticatory system works and some practice through repetition.
In this blog article, Dr. Peter Dawson responds to a comment made on a previous article. The following was the comment:
It has been demonstrated repeatedly since 1997 that the relationship of bruxism to chronic craniofacial pain is non-linear. [1-4] In fact, 20% of the Raphael, et al, pain sample showed no bruxism. Lavigne lists among his finest work the discovery that sleep bruxism begins from an open mouth position with the action of the depressors.  This is not an “occlusal” problem beyond tooth wear, should the patient so decide.
That being said, the nature of the pain is such, particularly as it relates to headache, that keeping the posterior teeth apart with an appliance can prevent headache. As Mahan and Alling pointed out in their text , we have known that since 1960. 
Sessle, Dubner and colleagues have shown repeatedly that the pain of chronic M/TMD is not inflammatory.  Masticatory muscles are fatigue resistant over time, [9, 10] and the excess substance found is glutamate, not hydrogen ions from lactic acid in chronic craniofacial muscle pain. 
The blog post of April 25 is not supported by the current science.
One of the most common mistakes I see in occlusal restorations is also the easiest mistake to observe. It is interference of the posterior teeth with the anterior guidance. A perfected occlusion allows the anterior teeth to contact in centric relation simultaneously, and with equal intensity with the posterior teeth. This harmony of contacts occurs with complete seating of the condyles at their most superior position, which is bone braced. This means that there is an ideal distribution of compressive contact starting at the TMJs, and continuing all the way through front tooth contact. This is the contact distribution that we want for centric relation.
When the jaw moves from centric relation, in a perfected occlusion only the anterior teeth contact. All posterior teeth distal to the cuspids should immediately separate. This is called "posterior disclusion". Separation of the posterior teeth should occur, whether the jaw moves forward or left or right from centric relation.
Dr. Dawson receives emails and letters from clinicians all over the world asking questions and looking for clarification on all matters of Functional Occlusion and challenges in dentistry.
From: A Dentist in Canada
Subject: Long Centric
Explanation of "Long Centric"
Assumption: Dawson centric relation is valid beyond a shadow of a doubt. My 37 years of successful clinical experience validates the truth of this assumption.
If I were writing the curriculum for a four-year dental education, I would start in the freshman year by asking the question, "How does disharmony between the TMJ's and the occlusion cause harm?" I would then tell every student that this question will be a dominant centerpiece for their dental education. I would let them know that during their four years, they will be expected to understand the answer to this question so clearly that when they start practice they will be at a tremendous advantage over more than 90% of the "usual and customary" dentists.
It is not possible to be a "complete" dentist without a comprehensive understanding of occlusion. Occlusion is the foundation for everything a dentist does that involves teeth. A thorough knowledge of occlusion is the basis for understanding why teeth get loose, why they wear excessively, break cusps, fracture restorations, or shift position. Occlusal disharmony is a primary consideration when dealing with sore teeth, sore muscles, and orofacial pain, including a high percentage of chronic tension headaches.
If the teeth are part of the mandible , and the mandible is one bone, don't the teeth and bone have to move in the same direction? If the condyle moves downward and backward, wouldn't the teeth have to separate during this movement as they would also be moving downward and backward? If the teeth are biting into the leaf gauge with their own closing muscle power, and the power is applied from behind the teeth, these two things seem to be mutually impossible to occur at the same time. Otherwise you are saying that the mandible can pivot with the teeth as the fulcrum.