Well, agree with Watchtower's application or not, it is a scripture and if they consider themselves to be teaching the truth, it is only appropriate that they use the scripture about those who once believed but now speak against them ... just saying ... I don't agree with them, but I don't see how they are misapplying it from their point of view.
NWT (1 Timothy 6:3-4) 3?If any man teaches other doctrine and does not assent to healthful words, those of our Lord Jesus Christ, nor to the teaching that accords with godly devotion, 4?he is puffed up [with pride], not understanding anything, but being mentally diseased over questionings and debates about words.
NIV 3 If anyone teaches otherwise and does not agree to the sound instruction of our Lord Jesus Christ and to godly teaching, 4 they are conceited and understand nothing. They have an unhealthy interest in controversies and quarrels about words that result in envy, strife, malicious talk, evil suspicions
New Living Translation 3 Some people may contradict our teaching, but these are the wholesome teachings of the Lord Jesus Christ. These teachings promote a godly life. 4 Anyone who teaches something different is arrogant and lacks understanding. Such a person has an unhealthy desire to quibble over the meaning of words. This stirs up arguments ending in jealousy, division, slander, and evil suspicions.
English Standard Version ... 3 If anyone teaches a different doctrine and does not agree with the sound b words of our Lord Jesus Christ and the teaching that accords with godliness, 4 he is puffed up with conceit and understands nothing. He has an unhealthy craving for controversy and for quarrels about words, which produce envy, dissension, slander, evil suspicions, 5 and constant friction among people who are depraved in mind and deprived of the truth, imagining that godliness is a means of gain.
New American Standard Bible ... 3 If anyone advocates a different doctrine and does not agree with sound words, those of our Lord Jesus Christ, and with the doctrine conforming to godliness, 4 he is conceited and understands nothing; but he has a morbid interest in controversial questions and disputes about words, out of which arise envy, strife, abusive language, evil suspicions,
Barnes' Notes on the Bible
But doting - Margin, "sick." The Greek word - νοσε´ω noseo¯ - means properly to be sick; then to languish, to pine after. The meaning here is, that such persons had a sickly or morbid desire for debates of this kind. They had not a sound and healthy state of mind on the subject of religion. They were like a sickly man, who has no desire for solid and healthful food, but for that which will gratify a diseased appetite. They desired not sound doctrine, but controversies about unimportant and unsubstantial matters - things that bore the same relation to important doctrines which the things that a sick man pines after do to substantial food.
Clarke's Commentary on the Bible
Doting about questions - He is sick, distempered, about these questions relative to the Mosaic law and the traditions of the elders; for it is most evident that the apostle has the Judaizing teachers in view, who were ever, in questions of theology, straining out a gnat, and swallowing a camel.
Gill's Exposition of the Entire Bible
but doting about questions and strifes of words: or he is "sick or diseased"; his mind is distempered; he is like one in a fever, that is delirious; his head is light and wild; his fancy is roving, and he talks of things he knows not what; his head runs upon "questions"; foolish and unlearned ones, about the law and works, and the necessity of them to justification and salvation; concerning genealogies, and other fruitless and unprofitable subjects:
Vincent's Word Studies
Doting (νοσω?ν)
N.T.o. Lit. sick. Comp. υ?γιαι´νουσι healthful, 1 Timothy 6:3.