This is what the WTBTS has printed about appointments.
"At the annual meeting held on October 2, 1944, in Pittsburgh, the members of the Pennsylvania corporation adopted six resolutions amending its charter. The charter had provided that voting shares be issued to contributors of funds to the Society’s work, but the third amendment eliminated that provision. A report on that annual meeting noted: “Membership in the Society will be limited to not more than 500 . . . Each one chosen must be a full-time servant of the Society or a part-time servant of a company [congregation] of Jehovah’s witnesses and must show the spirit of the Lord.”
Thereafter, directors of the Society were to be voted into office by individuals who were fully devoted to Jehovah, irrespective of the amount of money that they contributed to advance the Kingdom work........
In 1971 the same speaker explained that the members of the Watch Tower Society could not vote in the members of the anointed Governing Body. Why? “Because,” he said, “the governing body of the ‘slave’ class is not appointed by any man. It is appointed by . . . Jesus Christ, the Head of the true Christian congregation and the Lord and Master of the ‘faithful and discreet slave’ class.” Clearly, then, the members of the Governing Body cannot be voted into office by the membership of any legal corporation."
http://wol.jw.org/en/wol/d/r1/lp-e/2001051
"While directors of a legal corporation are voted into office by its members, the Governing Body is not appointed by any man but is appointed by Jesus Christ. There is no need for the directors of various corporations used by Jehovah’s Witnesses to be members of the Governing Body. At the recent annual meeting of the Watch Tower Bible and Tract Society of Pennsylvania, members of the Governing Body who were serving as its directors and officers voluntarily stepped aside from their positions. The vacancies were filled by mature brothers of the “other sheep.” (John 10:16) Thus the Governing Body can spend more time in preparing spiritual food and in otherwise caring for the spiritual needs of the worldwide brotherhood.—1/15, pages 29, 31."
According to this information the Directors of the WTBTS are voted in by the members of the WTBTS. The Governing Body is not voted in by any men which means their formation would not be established through the Charter or it's by laws.
How are Governing Body members elected? They won't say, well they do say, and it's by Jesus.
So how is the Governing Body of Jehovah's Witnesses recognized by the JWs? By their names being printed in WTBTS publications and through JW org, which are both controlled by the directors of the WTBTS.
If the Directors of the WTBTS decided that the current GB were not acting in harmony with the Charter and chose new members would this also be accepted by the JWs? When you are in control of the printing press, the media and all the assets it is a possibility.