In my opinion, the answer to the question of "Do Jehovah's Witnesses still care about the 'Truth'?" is "no". They do not. Here's why:
"The Truth" is a reference to the beliefs system and doctrines of the Watch Tower Bible & Tract Society. The Truth is not the truth. Truth is something that is factually correct and does not change. The Truth is the current explaination of the Bible as told by the Watch Tower Bible & Tract Society and changes on a regular basis (flip-flop).
There is only one thing about The Truth that active rank & file Witnesses care about and that is not being disfellowshipped. Oh, sure, most will openly state that they believe all the teachings of the Watch Tower and that the end is near, but most don't believe that or secretly disagree with their own teachings. If all current children of Witnesses refused to be a part of the organization and refused to raise their children in it, the Christian Congregation of Jehovah's Witnesses would fall apart within 10 to 20 years.
Current Witnesses are usually born-in and their entire support system of family and friends are Witnesses. They know if they stop being a Witness they will lose their entire support system. They are being kept in by coercion.