Yup, it's most likely fake. I've been investigating a bit more with the help of a jazz connoisseur friend (he hosts a radio show). We've found a playlist on Spotify including lots of tunes played on that TV show. doing a search over it I've found the tune that was sounding when that vinyl was supposed to be playing. It's a 2006 tune by a band named Five in Orbit, from their self titled album. If you feel curious, it's available on Spotify The only other chance that comes to mind is that the album and cover are legit, but for being copyright protected music, they played a tune by other unknown band having a lower royalties cost.