Genuine Fender J-Bass?

Hi all, first post although I've been an avid reader for years. This is the first time I've actually found the need to post anything, however, since my question wasn't answered by reading others'. I have what I think is a genuine Fender J-Bass body, but I just can't be sure.

The story is, I got the body of the bass for free from my best friend's brother, who said he bought it in the mid-to-late 90s as an actual Fender Jazz, but the headstock was broken off in a car accident. He didn't still have the headstock, but (what was left of) the rosewood neck was still attached. I took the body, added a maple Mighty Mite replacement neck, a Fender Jazz Bass decal and called it a day, because the tone of the thing sounded superb regardless of its authenticity.

However, as I was changing the tuning pegs today to the standard-issue Fender pegs, I got curious as to whether I could figure out if this thing was actually a legit Fender or not. So, I did some online research, and, using the serial number located on the body under the neck, I went to

The Guitar Dater Project - Fender Serial Number Decoder

which stated that, since I guess my serial number has no letter prior to the five digit number, the site assumed...

Your guitar was made at the
Fullerton Plant (Fender - Pre CBS Era), USA
in the Year(s): 1960 - 1961

However, I find this hard to believe, as the date under the serial number is 1995, as goes along with the original story of the bass.

I also know that the volume knobs aren't usually this style on the Fender Jazz Basses, numbered and such; what's normal is the black knobs with the white line. However, I also know that some of the 80s and 90s model J-basses were issued with these knobs, so maybe it's accurate? I really have no idea, so I need your help, fellow TalkBass members!

I've included pictures of both the bass and the stamping of the serial number/date on the body, so any help would be appreciated!