Good quote, and I more or less agree, although as ever it is a matter of perspective. Music is also about communiication.
The songwriter has his/her interpretation, which may also include an intended message to the listener
The performer can influence the message being delivered
The listener hears the message and then interprets it, leaving them with an understood meaning.
From the perspective of simply having an interpretation of the core song, there is no right or wrong.
However, from the perspective of "has the intended message been delivered and understood" then yes that could have been successful or not successful as a communication.
Songs can have different purposes:
If you are writing a song that is an issue song, intended to deliver a message to the listener, failure to deliver the intended message can be catastrophic.
if you are writing a song that is more abstract in nature, or simply tells a story with no real message attached, then communication of a set message is more or less unimportant.
there are no doubt more.
Every song will be a mix of purposes, each of which can be successful or not. For some facets of the song success in relation to the intents of the songwriter can be very critical, or not.