Is it true that if a member of the church of Christ is shown a truth from the Scriptures, they are bound to follow that truth?
Jesus said, "If you love Me, keep My commandments" (John 14:15). Hence, any true follower of Christ (a Christian) will strive to as obediently to the truth as they able to do so. This doesn't happen immediately upon becoming a Christian. The Scriptures speak of our growth in knowledge. "Therefore, laying aside all malice, all deceit, hypocrisy, envy, and all evil speaking, as newborn babes, desire the pure milk of the word, that you may grow thereby, if indeed you have tasted that the Lord is gracious" (I Peter 2:1-3). Therefore, as a person's knowledge and understanding improves, there will be adjustments as he conforms his life to the expectations of God. "Therefore gird up the loins of your mind, be sober, and rest your hope fully upon the grace that is to be brought to you at the revelation of Jesus Christ; as obedient children, not conforming yourselves to the former lusts, as in your ignorance; but as He who called you is holy, you also be holy in all your conduct, because it is written, "Be holy, for I am holy." " (I Peter 1:13-16).
One problem that arises is that many believe they understand the truth when then really don't. There are those who will only listen to the things they want to hear. "For the time will come when they will not endure sound doctrine, but according to their own desires, because they have itching ears, they will heap up for themselves teachers; and they will turn their ears away from the truth, and be turned aside to fables" (II Timothy 4:3-4). Others are attracted to lies because they have no desire to seek truth. "The coming of the lawless one is according to the working of Satan, with all power, signs, and lying wonders, and with all unrighteous deception among those who perish, because they did not receive the love of the truth, that they might be saved" (II Thessalonians 2:9-10). Still others distort the truth out of ignorance or willful disobedience. "And consider that the longsuffering of our Lord is salvation--as also our beloved brother Paul, according to the wisdom given to him, has written to you, as also in all his epistles, speaking in them of these things, in which are some things hard to understand, which untaught and unstable people twist to their own destruction, as they do also the rest of the Scriptures" (II Peter 3:15-16). Hence, a "proof" that satisfies you may be shown to be incorrect or inadequate by someone more familiar with the Scriptures.
If you are interested in a study on what constitutes good reasoning, may I recommend the study "Keys to Understanding" which is found on this web site. The later chapters especially focus on the many ways people abuse arguments to "prove" their points.