Question about best lap time trophy

[GarciaFever]

Ok so according to the trophy guide on PS3T, it says I have to beat all the best lap times for the original 28 tracks. I already have all DLC downloaded a while ago. Just around 20 minutes ago, I beat the best lap time on the last track that I needed, however I didn't get the trophy. That race I ended up placing 5th, but I figured that placement doesn't matter since all I need is to just beat the lap time. Is the game glitched, or do I have to actually place first in the race? If so, then this is some bullshit!

 

The lap that I beat the time on is the track where I have to get 4000 wallride points, and once I complete all 3 challenges, I can do a grudge race against the female character in pink.