Is the turn radius at fixed bank angle really independent of aircraft type?
If the turn is fully coordinated, turn radius at a given bank angle will depend on the speed of the aircraft and the local value of gravity.
This is because of simple vector and geometry: the vertical component of lift must still support the weight of the aircraft (whether that's a hang glider or an AN-225, a Helio Courier on the edge of stall or an SR-71), but the horizontal component, generated by the bank, produces a horizontal (=&gt; centripetal) acceleration that is fixed in relation to gravity for a given bank angle.
The problem is that this centripetal acceleration is determined by both turn radius and speed.  So, if your hang glider and your SR-71 want to make the same radius turn (within their usual flight envelope), they'll do it at wildly different bank angles.