I think they could be independent in a general sense, but I'm not certain on any specifics of that code that may further define independent.
A lot of it is going to be dependent on the size of your firm. I'd say, at a minimum, the person doing the review would have to be otherwise completely outside of any typical QC procedures. In other words: if this requirement were not in place, the person doing the review would have no involvement in the project. That could be a different project manager in your office, an engineer at another branch, etc.
If this were a review of a design failure, then it would absolutely need to be somebody with a financial interest in clearing your firm of wrongdoing (so it would have to be another firm in that case). But as a design review prior to submission, I don't think there is a conflict of interest. There may be an apparent conflict, though, so be sure to go out of your way to be transparent about who was involved with what and how they are to be considered an independent review.
So best case scenario would be hiring another firm to conduct the review, but I think it could work as an internal review with a "Chinese Wall" between the design group and the reviewing group/individual, breached only by the review itself.