KC-135's don't do reconnaissance. They do aerial refueling. They are based off of the Boeing 707 platform. Rivet Joint is also based on the 707, which is the RC-135.
Actually they are recce modified KC-135s. That’s how they started life, before they were converted. Many retained the boom operators station, although the boom had been removed.
The -135 and 707 are different airfames with a common ancestor, the Boeing Dash 80. The 707 was, in USAF service, used as the basis for the C-137 (including those used in the Air Force One role), the E-3 Sentry and E-8 JSTARS. It’s also used as the basis for the Navy E-6 Mercury airborne command and control aircraft.