I have two Fender Jazz Bass guitars. The one on the left is my Chinese Fender and the one on the right is my fretless Fender Jazz Bass, made in Mexico.
Are they REAL Fender basses? Yes, absolutely, authorized by Fender and made to specifications.
I purchased the Chinese Fender a few years back. My first bass guitar was a 1960 Fender Jazz Bass, purchased for me by my father. It too was sunburst with a tortoise shell pickguard. I was sentimental about it and wanting to replace it as closely as I could afford. The Chinese Fender only cost $500. It is a lovely three-color sunburst with a black pickguard.
I recently acquired the fretless Fender because I am now focusing on jazz. It only cost $650, and I bought it not for the excellent price, but for the availability. It came with a white pickguard, which I replaced with a tortoise shell pickguard. The tortoise shell looks much better on a sunburst finish.
If possible, listen to the videos and recordings with head phones, unless you have larger speakers attached to your computer. The small, built-in speakers in most computers cannot reproduce the bass or the warmth of the original recordings.
I play bass guitar and string bass in and around Hollister, California.