I am new on this board -- I actually found this thread while searching for "Tim Jordan" and Lansdale (the pastor and location of my former church). I am also young (I will be entering BJU as a freshman this fall) and potentially naive. However, I believe my perspective could still be valuable to the discussion. Here is how I see the BJU accreditation issue:
First of all, I believe that for BJU to seek accreditation is a positive step. When I was considering which college to attend, my decision came down to Clearwater and BJU -- both excellent schools. My career goal is to do research in artificial intelligence. Since this will require at least a master's degree, an important consideration was whether my graduate schools of choice (MIT and Carnegie Mellon) would recognize my undergraduate college's degrees. Since Clearwater is regionally accredited, this was a major advantage. BJU won my favor primarily because Clearwater's computer science and mathematics programs are still immature. Ten or fifteen years in the future, without BJU being accredited, I would potentially choose Clearwater over BJU (assuming Clearwater will not waver theologically and will continue to improve these majors). This is not to say I have any lack of respect for BJU; I greatly respect the college's fundamental positions and academic excellence.
I think BJU is making a wise move by accepting accreditation (insofar as TRACS is true accreditation). As Bob Jones (Sr., I believe) said, BJU has such high academics that they could join any accrediting association they wanted. While I understand BJU's hesitancy to do anything that would compromise their positions, I believe that accreditation (even regional accreditation) would help more than hurt. What would be necessary would be a binding, codified statement that would terminate the accreditation if the association attempted to force any antibiblical change upon the University. I do not know what BJU's legal structure is, but this could be done, for example, through an amendment to a charter or constitution.
As another poster wrote, I believe BJU has "painted themself into a difficult corner" by so dogmatically refusing accreditation in the past. If they admit they have changed their mind, they could (and would) be accused of compromise. On the other hand, if they continue their current course of essentially side-stepping the question, they will continue to be accused of hypocrisy. I believe that BJU's administration should offer a clear statement explaining why they believe TRACS accreditation is acceptable while regional accreditation is not. Their published statements do not offer a distinct exposition of this difference.
All in all, BJU's decision to seek accreditation is a step in the right direction. As others have pointed out, BJU is run by humans who can make mistakes. In terms of nondoctrinal positions, is it not preferable that if they reevaluate their positions and find them lacking, they modify them? To continue in knowingly wrong dogmatism is not only intellectually and morally dishonest but hurtful to past, current, and future graduates.