You have a bunch of confused concepts here. First, it is not true that all ringed gas giants have rings at such an angle to their axis of rotation. Take Saturn, for instance:
Image in the public domain.
See how its rings align with the horizontal cloud bands on its surface? The rings are clearly aligned with the axis of rotation, not at all like the situation on Neptune.
Another misconception is that Uranus's rings are tilted relative to its poles. This is not strictly correct; rather, Uranus is tilted relative to its rings. The reason for this is thought to be a collision between Uranus and another planet early in its life. The rings themselves formed much later.
Frame dragging is completely unrelated. It is more pronounced in the case of massive bodies rotating quickly; Uranus certainly does not satisfy the criteria for a major observable manifestation of this.
After your edit, I think I better understand what you're saying.
The reason that planetary rings are typically situated around the equator of a planet is because of their formation. One way that rings form is when a moon strays too close to its planet and is torn apart by tidal forces, forming one or more rings. Another way is when a planet pulls in extra matter from the protoplanetary disk, which can form a ring system.
In both cases, the source material is roughly perpendicular to the axis of rotation, and thus the rings form roughly perpendicular to the axis of rotation. Moons generally orbit in their planet's orbital plane, and planet axes are generally (but not always) closer to perpendicular than parallel to the protoplanetary disk.
Therefore, rings will form on the planet's equatorial plane.