that would fit the description given:

It is not sufficient to assume that standards will be applied. Neither should it be assumed that simply because the project was justified and effectively organised at the outset, this will continue to be the case. As the project progresses there must be regular assurance that:
a. the project is aligned with strategic and operational objectives;
b. an acceptable solution is being developed;
c. the solution continues to provide value-for-money;

especially this bit - which is in fact a quite important one:

Assurance covers all facets of a project, including business, user and supplier interests. All the aspects listed above must be checked throughout the project to ensure it remains consistent with, and continues to meet, a business need and that the validity of the project is not compromised by external changes. The responsibility for providing such assurance rests with the Project board.

The only rationale I can see for using "assurance" is to interpret this activity as "giving the assurance" to investors that the project is still worth pursuing IOW making sure that since the launch of the project there was no nasty surprises that would have rendered the project pointless (sudden changes in prices of inputs or finished products, or the worst imaginable scenario - some new competing technology that makes existing technologies terminally obsolete)