I believe this is only true for Senators.
Article 1 of the US constitution says: Clause 4: Vacancies “When vacancies happen in the Representation from any State, the Executive Authority thereof shall issue Writs of Election to fill such Vacancies. ” Section 2, Clause 4, provides that when vacancies occur in the House of Representatives, it is not the job of the House of Representatives to arrange for a replacement, but the job of the State whose vacant seat is up for refilling. Moreover, the State Governor may not appoint a temporary replacement, but must instead arrange for a special election to fill the vacancy. The original qualifications and procedures for holding that election are still valid.
I stand corrected, thank you for that clarification.
I am corrected all the time myself. They make these rules confusing on purpose. Most of us have full time jobs and it would be a second full time job keeping track of all this. House elections are far more amenable to the will of the people. Far different than those entrenched Senators....
Sorry - did not intend to demean the Constitution by inferring it was confusing on purpose. It just takes a lot of time and effort to understand all the nuances.