a significant flaw in Jehovah's Witness theology

I have an uncle and aunt and cousins who are Jehovah's Witnesses. I visited them recently and we got to talking about their beliefs. Not expecting to hit on something particularly profound, I told them how I have difficulty with their prohibition on government involvement (such as voting) -- that I think government involvement is a virtue. Interestingly, I found out I hit upon a fatal flaw in their worldview.

They explained to me that JWs believe the fundamental sin in the Garden of Eden was man rejecting God's governance, and that earthly governments are, by nature, the embodiment of a rejection of God's theocratic rule. They believe that at the end of time, God will destroy all government and establish His own government once and for all. They believe that our current time on earth primarily serves the purpose of proving to the heavenly hosts that man cannot successfully rule himself. So, to them, participating in government is to side with the enemy and contribute to the effort to prove God wrong. They get a lot of this from the admonition to be "in the world, but not of it." All of this, they believe, is the central theme of Scripture.

Before this came to light, I shared with them Romans 13:1-7:

"Let every soul be subject to the governing authorities. For there is no authority except from God, and the authorities that exist are appointed by God. Therefore whoever resists the authority resists the ordinance of God, and those who resist will bring judgment on themselves. For rulers are not a terror to good works, but to evil. Do you want to be unafraid of the authority? Do what is good, and you will have praise from the same. For he is God’s minister to you for good. But if you do evil, be afraid; for he does not bear the sword in vain; for he is God’s minister, an avenger to execute wrath on him who practices evil. Therefore you must be subject, not only because of wrath but also for conscience’ sake. For because of this you also pay taxes, for they are God’s ministers attending continually to this very thing. Render therefore to all their due: taxes to whom taxes are due, customs to whom customs, fear to whom fear, honor to whom honor." (emphasis mine)

What I said to them was, it seems bizarre to me that a church body would forbid its members from participating in something the Apostle Paul refers to as a "ministry."

We discussed the issue at some length, but in the end they warned me not to base my beliefs on an idea found only one place in the Bible. (In reality, I think the rest of Scripture harmonizes quite comfortably with this passage. Consider all the men of God in the Old Testament who worked in government. And consider that nowhere in Scripture is there a command against government participation. And I can see no necessity to interpret "of the world" as meaning government involvement any more than I can see "of the world" needing to mean something like commerce -- something the JW's have no issue with. We know from its usage in Scripture that the term "of the world," or "worldliness," refers to the sinfulness the world is entangled in. We are told to be "in the world," but not tied up in sin.)

"Hmmm. Are you saying that this passage of Scripture is inaccurate and its teaching can’t be relied upon? Does its message differ from the Watchtower's?”

What I find particularly interesting is, I have never heard this used as a challenge to JW theology. I think it hits upon a significant vulnerability. There is no way I can buy the idea that the Apostle Paul would have written the above passage had he believed government, as an institution, was fundamentally an embodiment of rebellion against God.