From part 2 of the Scottish Outdoor Access Code
A summary of your access rights
5. The main places where access rights do not apply are:
…..golf courses (but you can cross a golf course provided you don’t interfere with any games of golf);
……
From my conversation with a Fife Council access officer a few years ago about a minor issue on a core path next to a golf course “you can cycle on a golf course provided you stick to the tracks and don’t cycle on the greens or fairways”
As far as I can see you are correct.