Sorry, but you are quite wrong on this.

Star Gold access to lounges applies only to Star Alliance specifically designated lounges (most are, however). More importantly, it only comes into play for Star Gold members flying in economy.

Completely separate set of rules if you are in C or F. Status no longer matters. That C or F boarding pass alone gets you and one guest into the lounge of any Star Alliance carrier operated lounge for a same day departure.

For an easy example, the Silver Kris lounges at Changi are not designated Star Gold lounges (they send you to the SATS lounge instead if you are Star Gold and flying in Y). However, if you are flying outbound on, e.g., United in C or F, you can access the Silver Kris lounge in the C or F section of the lounge, respectively.