Yes, that IS a false dichotomy. Look, we all know my ecclesiology is somewhat Bohemian, but let's face facts.
First of all, the Lord's Spirit can, does and is often pleased to dwell within people whose gatherings and associations have become highly structured. Secondly, structure (organization, rules, custom, tradition, hierarchy, etc) has never been THE thing that quenches the Spirit or restricts its wider flow among all of Christ's people. Obviously, MANY things quench the Spirit. But - if it's done well - a positive, flexible structure can actually facilitate MORE of that every-member functioning which ought to exist.
No, human structure is not always the enemy of God's Spirit. It can become that, but so can a lot else. One particular thing about structure, however, is that we tend to establish structures aiming to permanentize them as well. Thus, once any structure becomes a real problem, it's usually also a permanent problem. Lifeless churches remain undead zombie churches. (World without end, amen.)
But that's still not the worst thing of all.
These heavily structured and seemingly zombie-fied versions of Christendom have become so common, they long ago began to present themselves as the norm. That not only perturbs both God and unbelievers, that often leaves the passionate remnant of any community far too likely to find themselves resisting the wrong thing.