Do silver crowns count towards the giant crown trophies?
According to multiple places, the first trophy for the giant crowns is the only one that can be unlocked by hunting a silver giant crown monster. The other two trophies require the giant crown to be gold.
From this thread, it looks like the trophy description was not fully translated and caused ambiguity. The trophies for hunting 10 and "almost all" giant crown monsters require the giant crown to be gold, even though the trophy for killing one giant crown monster can be earned for hunting a silver giant crown monster.
You can see this yourself if you change list language to Japanese on PSNP then use google translate on the page. It appears whoever translated the list to English omitted the part that includes the distinction on what crowns are required for each trophy. Bronze Giant Crown trophy specifies it pops from your first silver or above (gold) crown, but the silver (if google translate worked properly) and gold trophies specify gold crowns are required.