Sounds right to me, I recall the Jazz neck being part of what made it a Special, not just this Squier but many/most FMIC P/J precisions have seemed to have Jazz-sized necks.
The active P/Js
have four knobs and a jack on the bottom but the Squier in question was passive, wired vvt with a jack on the bottom. They stayed that way through many versions of Squier by Fender and Squier Standard series.
Just as a note the new Squier VM Precision PJ is not called a special and does not have a Jazz neck on it.