tl;dr Trajectory issues were considered in the failure investigation but were determined to be non-contributing.
While the physical cause of the Columbia accident (damage to the thermal protection system from an impacting chunk of foam shed from the External Tank) is well known, other causes were considered and eliminated during the investigation.
The methodology used was construction of a "fault tree", described here in Columbia Accident Investigation Board (CAIB) Report Volume 1, Chapter 4:
The NASA Accident Investigation Team investigated the
accident using “fault trees,” a common organizational tool
in systems engineering. Fault trees are graphical representations of every conceivable sequence of events that could
cause a system to fail. The fault treeʼs uppermost level
illustrates the events that could have directly caused the loss
of Columbia by aerodynamic breakup during re-entry. Subsequent levels comprise all individual elements or factors that
could cause the failure described immediately above it. In
this way, all potential chains of causation that lead ultimately
to the loss of Columbia can be diagrammed, and the behavior
of every subsystem that was not a precipitating cause can be
eliminated from consideration. Figure 4.1-1 depicts the fault
tree structure for the Columbia accident investigation.
CAIB Appendix D03 lists all the possible causes from the fault tree that were eliminated as potentially contributing to the failure. "Incorrect trajectory" was considered and eliminated: four trajectory-related entries are listed in the fault tree by "Fault Tree Element" name and description (apologies for all caps - direct quote).
- AC - AERODYNAMIC BREAKUP DUE TO IMPROPER ATTITUDE / TRAJECTORY CONTROL
- ACCF - IMPROPER ATTITUDE/TRAJECTORY CONTROL DUE TO COMMAND FAILURE
- ACEF - IMPROPER ATTITUDE/ TRAJECTORY CONTROL DUE TO CONTROL EFFECTOR FAILURE
- SFOML-WING-7-14 - HIGHER HEATING DUE TO OFF NOMINAL TRAJECTORY
Note that a white background in the following images means the cause was eliminated.