A possible scenario:
As noted by others, there was an FAA Airworthiness Directive, which read, in part, as follows:
On August 18, 2000, we issued AD 2000-17-05, Amendment 39-11879 (65 FR 51754, August 25, 2000), for certain The Boeing Company Model 767-200, -300, and -300F series airplanes. That AD requires a one-time functional check of the shear rivets in all six PCA bellcrank assemblies to determine the condition of the shear rivets; and replacement or rework of the bellcrank assemblies, if necessary. That AD resulted from reports that elevator bellcrank assemblies with failed shear rivets had been found on three Model 767 airplanes. We issued that AD to detect and correct any failed or partially yielded shear rivets of the elevator PCA bellcrank assemblies. Failure of two bellcrank assemblies on one side can result in that single elevator surface moving to a hardover position, independent of pilot command, resulting in a significant pitch upset recoverable by the crew. Failure of three bellcrank assemblies on one side could result in loss of control of the airplane.
Others have noted the possibility that the failure was related to the problems identified in this series of Airworthiness Directives; perhaps the prescribed fix was in some way inadequate.
So, a possible scenario that seems to fit the events:
1. Atlas 3591 departs Miami bound for Houston. Unbeknownst to the crew, one bellcrank assembly in the tail has previously failed and two others are in poor condition.
2. Captain's voice to Houston ATC: "Good afternoon, Giant 3591, 17.8, descending via the LINKK and we have Sierra." The FO is flying the airplane on this leg; the Captain is handling radios. So far, all is well.
3. At 18:37:31Z, at approximately 7,000' while flying the approach pattern for IAH, a second bellcrank assembly fails, resulting in a significant pitch upset. The captain takes control; the FO switches to radio duties. The captain pulls back hard on the yoke and recovers control, actually gaining altitude briefly before returning to the planned level. The failed assembly puts additional pressure on the other two assemblies, which are now nearing failure points.
4. The captain continues flying the airplane and working to diagnose the problem; he executes a left turn to verify that he has sufficient control. Control is satisfactory, but the crew is a bit concerned.
5. The FO, now handling radio duties, begins a conversation with ATC regarding diverting around some thunderstorms.
6. At 18:38:36, about one minute after the first bellcrank assembly failed, with the aircraft at about 6,000 feet in altitude, a third assembly begins to fail; the captain again fights to maintain correct pitch, again briefly gaining some altitude before returning to the pattern altitude. This occurs during the FO's last transmission, which sounds a bit rushed and possibly stressed.
7. At 18:38:46, the third bellcrank assemfly fails completely, leading to a sharp pitch-down attitude and resulting in complete loss of vertical control of the airplane. The crew, focusing entirely on saving the airplane, makes no additional radio calls.
8. The airplane impacts the ground at high speed.
Obviously this is entirely speculative, and even if some of it turns out to be right, most of it will probably turn out to be wrong. Just an effort to come up with *a* scenario that could fit the facts.