They probably did it for the exact purpose they claim, initially. Once they became an Associate member of the United Nations Department of Public Information (UN/DPI) they discovered ways in which the association provdided them leverage and opened doors that had been closed formerly. Seeing the other open doors, they walked through.
However, for me the biggest concern is that even at this late date when there is no longer any excuse for them to believe they "registered" and at which point they should know for certain they were an Associate member of the UN/DPI, they still lyingly claim to inquirers that they "registered" and eventually "withdrew [their] registration" which is not possible. There is no registered status with the UN/DPI Non-Governmental Organization (NGO) Section, there is only an Associate membership status.
So even if we discount the fact of it having happened as accidental, there is no way to discount continuing to lie about what actually occurred.
It is important to remember when speaking of this that they did not become a member of the UN. They became a member of the UN/DPI, which is, in its own right, "a secular organization that has objectives contrary to the Bible" and is "under judgement by Jehovah God"—nothing compelled them to join, they joined out of their own desire to enjoy the privileges they believed to accompany a membership to the UN/DPI.—Organized to Do Jehovah's Will (2005) p. 155 par. 2
They do not admit to becoming a member of the UN/DPI, they do not admit that it was gross wrongdoing even when asked directly, they instruct elders to tell those (like myself) who ask that they should be content with the explanation provided and wait on Jehovah, they deceptively avoid their culpability, they do not attempt to right the wrong, they are quite obviously unrepentant of their actions.
Romans 2:1-11—Therefore you are inexcusable, O man, whoever you are, if you judge; for in the thing in which you judge another, you condemn yourself, inasmuch as you that judge practice the same things. 2 Now we know that the judgment of God is, in accord with truth, against those who practice such things.
3 But do you have this idea, O man, while you judge those who practice such things and yet you do them, that you will escape the judgment of God? 4 Or do you despise the riches of his kindness and forbearance and long-suffering, because you do not know that the kindly [quality] of God is trying to lead you to repentance? 5 But according to your hardness and unrepentant heart you are storing up wrath for yourself on the day of wrath and of the revealing of God’s righteous judgment. 6 And he will render to each one according to his works: 7 everlasting life to those who are seeking glory and honor and incorruptibleness by endurance in work that is good; 8 however, for those who are contentious and who disobey the truth but obey unrighteousness there will be wrath and anger, 9 tribulation and distress, upon the soul of every man who works what is injurious, of the Jew first and also of the Greek; 10 but glory and honor and peace for everyone who works what is good, for the Jew first and also for the Greek. 11 For there is no partiality with God.