Contrast the following two cases, in which X is essential for plaintiff's case:

I. One of plaintiff's witnesses testifies that X happened, and defendant makes an explicit argument of recent fabrication. The plaintiff then offers a consistent statement that the court admits under 801(d)(1)(B).

II. One of plaintiff's witnesses testifies that X is true. Defendant introduces evidence of a prior inconsistent statement, arguing that the witness is unreliable. Plaintiff then seeks to introduce a prior consistent statement, to attempt to show that it is unlikely that the witness made the prior inconsistent statement. The court rules that the statement is admissible under Federal Rule of Evidence 613.

Which (if any) of the following statements about possible differences between the cases are true, and which (if any) are false?