The case
Thousands of people remember renting it: the VHS box, the purple genie outfit, the two kids, the wishes. Some remember watching it with a sibling. The trouble is that the movie was never made, never shot, never released, and its supposed star has spent years politely saying so.
What does exist is "Kazaam," the 1996 Disney-distributed film with Shaquille O'Neal as a rapping genie. Sinbad, meanwhile, was everywhere in the '90s: sitcoms, movies, hosting, and he did dress in costume to host a 1994 TNT movie marathon. Somewhere in that soup, a film assembled itself.
Why our brains do this
Two real things, Kazaam and a very famous comedian with an Arabian Nights name, blended into one plausible memory. Once one person described the "movie" online, others recognized it and filled in details.
Sources: Wikipedia — Kazaam · Wikipedia — Sinbad (comedian) · Wikipedia — False memory: the Mandela effect