[4] The song dealt with Bowie's feelings for his schizophrenic half-brother Terry Burns, who had died by suicide on 16 January 1985 when he walked in front of a train at Coulsdon South railway station, having previously been held in Cane Hill Hospital.

A striking video was shot by Mark Romanek, depicting Bowie as a businessman paranoid of his colleagues, who seemingly conduct experiments on him and find him a disturbing influence, forcing him to jump from the roof of the corporate building to his death.

New collaboration with "Let's Dance" co-producer Nile Rodgers has the potential to meet with similar top 40 approval, although innovative batch of remixes is already shaping up to be a club favorite here and abroad.

[9]Jon Selzer from Melody Maker complimented the song as "sophisticated, mock-wayward funk, pretending it's balancing precariously over a tightrope when it's really on solid ground."

"[11] Parry Gettelman from Orlando Sentinel felt that jazz trumpet player Lester Bowie's brief entrance "enlivens the otherwise pastel "Jump They Say", which recurs as a remix toward the end of the album.

"[12] A reviewer from Philadelphia Inquirer constated that Bowie "reaffirms his commitment to arty dance-rock",[13] while Reading Evening Post complimented the song is "surprisingly good".

[15] In a 2017 retrospective review, Quentin Harrison from Albumism noted that "that romantic energy" from Bowie's marriage to Iman "put a skip in the sonic step of some of the set's darker material", like "Jump They Say".

"[16] Stephen Thomas Erlewine from AllMusic remarked the "paranoid jumble" of the song, naming it one of the "moments" from the album, that "are the first in a long time to feel classically Bowie".