Chevron isn't getting direct access to a big e-mail database. Plaintiffs' lawyers will do the search and produce to Chevron only what's relevant, not privileged, not confidential, etc.
To be clear, I mean the counsel representing the activists will do the search and give only relevant documents to Chevron. Since the activists are adverse to Chevron, it wouldn't be appropriate for Chevron's counsel to go through the emails themselves.