Not true. Please recall that the U.S. has two judicial systems, state and federal. Federal judges are appointed by the President (Executive Branch) and confirmed by the Senate (Legislative Branch) and are (with some exceptions) appointed for life terms. No elections there. At the state level, YMMV (some states have partisan judicial elections, some non-partisan judicial elections, and some have judges appointed by the governor for life terms.

Westlaw does more than just match up page numbers. They have a copyrighted "Key" numbering system that indexes case law by each point of law. This is not done by the court system (state or federal). West employs editors (most of whom are lawyers, IIRC) to read the cases and create the index/key numbering system. West does have their own pagination system (called "pin-point" cites), as does Lexis, but that's not why the Westlaw copyright was upheld. In fact, if you print off a case/statute on Westlaw, it will come with a footer on the page that DISCLAIMS any copyright on original govermental work (i.e., the actual text itself of the case or statute).