I don't think wortsgen HQ purposely spread wrong info. As SdFear said, they probably don't get full context of the spoils.
But yeah WG make it look like Zoro was surprised at what chopper did and he himself fail to take out the giants which wasn't the case.
Also it was jimbei not sanji holding killingham's head and it felt like it was a team effort and not something sanji did solo (though he could have done it solo).