I want to see a newspaper from 1902. According to OskiCat, the Bancroft Library has an "archival negative" which is "restricted." Can the public come in and view the archival negative?

The public is indeed able to come to the Bancroft Library and access "restricted" archival negatives in microfilm form (see this OskiCat results example). Restricted archival negative microfilms are also eligible for Interlibrary Loan with other institutions, so that may be another option if your local library participates in Interlibrary lending. The Bancroft Library can be contacted directly at (510)642-6481, or at bancref@library.berkeley.edu.