This article contains Watchtower quotes about obedience to Jehovah AND 'His Organization'. At the same time they teach that Jehovah requires 'exclusive devotion'. What they really mean is there's no difference between loyalty to Jehovah and loyalty to the Watchtower. Exclusive devotion to Jehovah is the same as exclusive devotion to the Watchtower organization.
Consider the facts and what the Watchtower says.
The Watchtower uses God's name Jehovah when referring to themselves! Instead of saying, 'the Watchtower requires loyalty', they say 'Jehovah requires loyalty'. They are speak for God even though they admit having no divine inspiration and mistakes are possible.
When Jehovah's Witnesses 'obey Jehovah' they are obeying the Governing Body of Jehovah's Witnesses (8-12 men+-) who are imperfect and make mistakes.
The truth is that Jehovah's Witnesses 'run ahead of Jehovah' every time they obey the Watchtower. Instead of praying to God and waiting for Holy Spirit to answer them, they pray to God and run to a Watchtower publication that quickly gives them the 'correct' answer. The problem is that sometimes God's plan for us is not the same as what the Watchtower currently teaches. What the Watchtower says is 'the truth' today, might not be the truth tomorrow.
'Peter and the other apostles replied: "We must obey God rather than human beings!' Acts 5:29
'a limited number of anointed men have the responsibility of representing the slave class. They make up the Governing Body of Jehovah’s Witnesses. ... Whether we are “domestics,” who are part of the anointed remnant, or we are members of the great crowd, let it be our determination to cooperate fully with the faithful steward and its Governing Body.' Watchtower June 15, 2009, Article: 'The Faithful Steward and Its Governing Body.'  
'By word or action, may we never challenge the channel of communication that Jehovah is using today. (Num. 16:1-3) On the contrary, we should cherish our privilege to cooperate with the slave class. And should we not strive to be obedient and submissive to those taking the lead in our local congregation?' Watchtower Nov 15, 2009, article, 'Treasure Your Place in the Congregation', par 5. In the same article, the organization cautions Jehovah's Witnesses against disobedience, disrespect, and a spirit of independence. JW's are told to be obedient and submissive to those taking the lead.
'Those with an earthly hope should, therefore, recognize Christ as their Head and be submissive to the faithful and discreet slave and its Governing Body and to the men appointed as overseers in the congregation.' WT, Oct 15, 2009, Article: 'Be Aglow With the Spirit', par 10
'God sees their imperfections more clearly than any human can. Still, he expects us to be submissive. Cooperating with the elders, even though they are imperfect, gives evidence that we accept Jehovah’s authority.' WT, June 15, 2008, Article: 'Accept Jehovah's Authority', par 15
'We must serve Jehovah with his spirit-directed organization.' WT, Jan 15, 1997, Article: 'What Does God Require Of Us?', par 21
'Today, God does not speak to his servants directly as he did to Job. Instead, he reproves them by means of his Word and his spirit-directed organization.' WT, June 1, 1993, Article: 'What Does It Take To Make You Happy?', Subtitle: 'Accepting Divine Reproof', par 2; See Spirit Directed Organization
Obeying the Watchtower is required if you're a baptized JW. It's not an option. Most JW's are not aware of this. Because the truth is hidden, JW's believe they obey the Bible and Jehovah, - not the organization.
WT rules and consequences of disobeying the Watchtower are found in the secret Watchtower publication for Elders, Shepherd the Flock of God
What is the punishment for disagreeing with the WT? Watch this video
1. 'anointed men', 'domestics', and 'anointed remnant', refers to JW's who believe they are going to heaven. The 'great crowd' refers to millions of JW's who believe they'll live forever on a paradise earth. The 'faithful steward' ultimately refers to the Watchtower and it's Governing Body, which is commonly called God's 'faithful and discreet slave' based on a parable of Jesus in Matthew 24:45-51
2. JW's believe that the Watchtower's Governing Body must be obeyed because they represent the 144000 anointed JW's who go to heaven to rule the world armageddon. Interestingly though, the Watchtower says that due to past religious beliefs, mental or emotional imbalance, some JW's might mistakenly believe they are anointed.
The Watchtower says, 'A number of factors—including past religious beliefs or even mental or emotional imbalance—might cause some to assume mistakenly that they have the heavenly calling. We thus have no way of knowing the exact number of anointed ones on earth; nor do we need to know.' WT, Aug 15, 2011, page 22
Based on what the Watchtower says, just because someone claims to be anointed doesn't mean they are. They could be mistaken. Thus even though the Governing Body of JW's claims to be anointed, - doesn't mean they are.
3. Claims about being anointed and chosen by God to rule the world might be sincere based on a lifetime of religious tradition or it might be a strategy to control minds.
4. The Watchtower claims to be God's exclusive spirit-directed organization and channel of communication. Since 1925 the Watchtower has given JW's only two choices, - the Watchtower or Satan's organization (everyone else). However on rare occaisions in their literature the Watchtower admits having no divine inspiration. They also caution JW's about resisting Satan which means Watchtower followers are not immune from the temptations of Satan. Everyone in the world regardless of religion has the potential to be examples of God's love or hateful and unkind like Satan. (See Watchtower quotes about hatred of JW's who leave the WT.) What is the truth? The Watchtower says, 'No harm is practiced, however, by withholding incriminating information from one who is not entitled to know. ... Various characters of the Bible have been accused of lying, such as Jacob, Rahab, the Gibeonites, David and others, but there is no record in the Bible that they came under divine disapproval for this.' Watchtower Oct 1, 1954, 'Christians Live the Truth', par 21, 25. Read more Watchtower quotes about when it's ok to be 'shrewd' and less than 100% honest.