Your comment is mostly accurate. However, I'd imagine anyone hearing a message was sent through SWIFT would assume a protocol got it to SWIFTnet followed by their own systems processing it. The two are inseparable. We used to call this sort of thing a "system of systems."

Anyway, it's accurate to think of protocol + SWIFT's mgmt systems as "the SWIFT system" given they work collectively to hanndle a SWIFT transaction.