The way it's supposed to work is:
If it's a badge, the game will only keep track of the first time you earn it, obviously.
If it's a medal, the game will always keep track of the first time you earn it, and then also every subsequent time you earn them UNLESS you also got a medal that is strictly better (such as getting a compet-n platinum making you ineligible for a compet-n gold)
I just did a 7 minute run of ITYTD and confirmed this. This must've been your first speedrun, like the speedrun bronze medal suggests.