This was an odd statement either way. The Governing Body is saying they are not lead by God nor capable of being right when it comes to doctrine.
The theological term "inspire" as in "inspired by God" means to be "guided by God." To say the Governing Body is not inspired is to say it is not "guided by God. "
The theological term "infallible" does not have anything to do with perfection. In reference to religion, the term means to be "incapable of teaching false doctrine and morals." The term was coined by the Roman Catholic Church and describes not the Pope (as Witnesses so ignorantly mistake that it does) but the authority a Pope can take to speak on behalf of the Church when it, as a whole, comes to a decision on doctrine of morals.
For instance, if a matter never explicitly defined in the Church as doctrine becomes a matter of question in the Church, the Pope can assign theologians, lay persons, and experts on the matter to research and come to a conclusion. If the debated subject is proven to be a matter of faith or a moral stand the Church has had since its beginning, though not explicitly so, the finding will be presented to the Pope to declare it dogmatically to preserve it from further question. This DECLARATION that the doctrine or moral teaching is true or valid as a dogma of the Church is then considered infallible by the entire process when announced by the Pope. The Pope himself is not infallible nor can be teach or invent new doctrine, but can only pronounce such matters of faith and morals as dogma when the Church agrees it is so. In 2000 years this has only occurred twice.
Thus to say they are not "infallible," the Governing Body is saying they cannot be right nor ever possess the faculty for being right on matters of morality of doctrine.
Seeing the simplified version demonstrates that they don't know the actual meaning behind either term.
Why join a religion like that? It has absolutely nothing to offer.