There is no need to repeat what has been more than sufficiently stated on the other thread - but again, an apparition is not deemed acceptable by default, rather for an alleged apparition to be accepted as authentically supernatural, and deemed worthy of credence by the Catholic Church, the standard of proof is high.
First, there often is some sort of supernatural confirmation that the message is indeed from heaven, and not owing to something within the power of nature, or to human beings deceiving or being deceived. Think of, for example, the Tilma that Our Lady of Guadalupe gave St. Juan Diego, that even to this day completely astounds secularist scientists, and was instrumental in the Bishop recognizing it truly was from Heaven. Second, and no less important, the "seers" must distinguish themselves by an exemplary life, and the practice of virtue in the highest degree, usually in such a way as is admitted by opponents, and which leads other souls to conversion to God. Saints who received genuine apparitions routinely demonstrated the greatest piety in their personal lives, beside announcing some miraculous act performed by Heaven, as even their opponents admitted. Not only did 70,000 eyewitnesses see the Miracle of the Sun as announced by the three saintly Fatima children, but even the Marxist press did not deny the piety and sincerity of the children, and moreover the miracle happened at exactly the prophesied time, astounded the godless skeptics present, and led to the conversion of several faithless men.
Personally, while I do not pass judgment on the personal motives of the seer and do not need to, I think all Catholics can easily have moral certitude that these particular "apparitions" are not from the Blessed Virgin, in the same way we can have that same certitude concerning many other recent alleged "apparitions". No apparition is presumed supernatural until proven otherwise, quite the contrary. It is a capital mistake for His Excellency Bishop Williamson to give to these messages anywhere near the same credence Catholics have always given to the approved apparitions. When Heaven speaks, men need to obey, certainly. When someone misspeaks in the name of Heaven, in Heaven's name, do not obey them.