The Short Version
Research confirms that elephants produce some vocalizations — particularly infrasonic rumbles — using the same vocal-fold vibration mechanism as human speech and singing. However, describing elephant communication as "singing" overstates the evidence. Scientists use "singing" as an analogy for the shared production physics, not as a validated behavioral classification. The only peer-reviewed paper in the evidence pool does not label elephant vocalizations as singing, and most supporting sources are press rewrites of a single 2012 finding about sound-production mechanics.