You're right, and in fact the high elf queen never did give a kill order. But the fairies know who she is, and that she's not liked by the queen. So they take it on themselves because they feel their actions will be rewarded (they won't be). Just loyalist brainwashing.
Murdering Sylvia would absolutely call unneeded attention, which is exactly why she was sent to Syl'anar on a "mission" (to never be seen again)