Alan Leeds is indeed misremembering.
A visit to PrinceVault's page for Jill Jones reveals Prince was deeply involved in that album:
All of the eight tracks were written by Prince (although he was listed as co-writer only on five, with Jill Jones taking credit for seven of the tracks), and seven of the tracks feature his input musically.
The page further details:
The tracks were recorded between July 1982 and October 1986. Many of them were initially recorded by Prince before lead vocal overdubs by Jill Jones were added.
There are also plenty of unreleased tracks resulting from the sessions:
In May 1985, Prince and Jill Jones recorded "My Man" together, as work on her album began in earnest. Later in May, Prince and Jill Jones recorded several more tracks for the album: "Come Elektra Tuesday", "Married Man", "Killin’ At The Soda Shop", "Living Doll" and "For Love", of which "For Love" is the only track included on the album.
In August 1985, Prince and Jill Jones recorded "My Sex" for the album, which was at one point considered as a title track for the album, but later rejected, and revised "Mia Bocca", "G-Spot" and "Baby, You’re A Trip". Prince worked further on many of the album’s tracks in January 1986.
In February 1986, "Euphoria Highway" was recorded for the album, but was later rejected. In late February, the first configuration of the album was compiled, but the tracklist of this configuration is unknown. "Violet Blue" was later recorded, in October 1986.
Arguably, Prince and Jill Jones recorded at least two albums worth of music. Not exactly something I'd describe as "very little involvement". Moreover, Prince was deeply involved until the very end:
Prince worked on overdubs and mixing in November 1986, with an album sequence compiled on 12 November 1986, and no further work is known to have been done on the album, indicating that this configuration may have been the final, released, version of the album.
(Note that details about much of Prince's work for that album will be available in Duane Tudahl's upcoming book Prince and the Parade/Sign O’ The Times Era Studio Sessions: 1985-1986.)
It should be noted that in that same article Alan Leeds also misremembers Prince's input on the first album Mavis Staples recorded for Paisley Park Records:
She was at a lull in her career and Prince thought it was a tragedy that she didn't have a deal. He did a couple of tracks and then passed it on — which is, inevitably, what happened with every project. She ended up doing most of it in Memphis with people she knew down there.
PrinceVault offers the following information about Time Waits For No One:
Six of the album’s eight songs are written, produced and largely performed by Prince ("Interesting", "Come Home", "Jaguar", "Train", "I Guess I’m Crazy" and "Time Waits For No One").
Again, not something I'd describe as "very little involvement".
Note that there are two album tracks which did not involve Prince at all, as well as two B-Sides:
Al Bell and Homer Banks wrote and produced (with Lester Snell) the two other songs ("20th Century Express" and "The Old Songs") and the two non-album tracks "Land Of Ecstasy" (released as the b-side of "Jaguar") and "All The Discomforts Of Home" (released as the b-side of "20th Century Express").
It should however be noted that Prince and Mavis Staples did not work together in the studio on the album: she recorded all her lead vocals on her own.
Even The Voice, her second album for Paisley Park Records, features plenty of input from Prince:
Eight of the album’s twelve songs are written by Prince (two of which, "Melody Cool" and "Positivity", had previously been included in different forms on albums released by Prince), and he appears as a musician to varying degrees on some of the tracks also.
So it appears that Leeds's memory is failing him somewhat when it comes to these albums. Then again, this is about events that happened 35 years and more ago, at a time when Prince's studio work was at a stunning pace (one of the reviews for Duane Tudahl's upcoming book mentions that it documents about 320 studio sessions for 1985-1986) and Alan Leeds was (likely) less involved with the label.