I'd like a lawyer to chime in, but if they have previously made statements that could be exculpatory, I think Brady v. Maryland may apply. The point is to give the defense time to prepare, so they aren't ambushed at trial.
The notes to Rule 16 discuss the Constitutional issue:
> The Committee recognizes the force of the constitutional arguments advanced by defenders. Requiring a defendant, upon request, to give to the prosecution material which may be incriminating, certainly raises very serious constitutional problems. The Committee deals with these problems by having the defendant trigger the discovery procedures. Since the defendant has no constitutional right to discover any of the prosecution's evidence (unless it is exculpatory within the meaning of Brady v. Maryland, 373 U.S. 83 (1963)), it is permissible to condition his access to nonexculpatory evidence upon his turning over a list of defense witnesses. Rule 16 currently operates in this manner.
Note that the notes discuss a house version of the rule that included a provision requiring both sides to, at the defense's option, turn over witness lists 3 days before trial. That provision ultimately did not make it into the final rule.
