IMO the issue was not one of confusion with the command structure (which was well understood by all) or prioritising incoming wireless messages, for which there was a protocol (with navigation related ones taking priority over private messages), but the difference in perception of wireless messages between the operators and the ship's Captain/Officers. In 1912 shipboard wireless telegraphy was still bit of a novelty and despite incedents such as the Binns/Republic one, its importance was not yet fully appreciated by all concerned. People like Captain Smith and to some extent even his Officers would have risen in the ranks without any experience of this technology till the start of the 20th century and so better versed with other forms of communication. Even after the Marconi Company was established and use of wireless telegraphy became relatively common, the service would have remaind something of a novelty in the senior officers' minds and its importance might not have been prioritised in their pre-trained minds.
On the other hand, most wireless operators like Phillips and Bride were young, learned about the new technology whilst in their late teens and trained specifically for its use. Many of them might not have had the "natural born sailor" turn of mind and added to that was the fact that they were empoyees of the Marconi Company rather than the shipping line. But once on board a ship, they would have come under the Captain's overall command and the use of their equipment would have been according to the protocol. It is possible that in 1912 this relationship was still not fully grounded and depite existence of a clear protocol, there could have been differences in the manner by which things like ice related messages were perceived. Those perceptive differences might have been the reason why Captain Smith stopped short of issuing specific orders to his wireless ops that all ice related messages relevant to the Titanic's route should be sent to the bridge; it may also have been one of the reasons why Phillips and Bride did not do so off their own back.