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That’s a mystery which may defy solution until someone figures out time travel. I mean, we’re all time travellers, but time travel in the opposite direction. :’) The reason for the lack of consensus on the Uranian tipped axis is that the Uranian moon system is the most normal of any in the Solar System, at least among the four known gas giants. Almost any mechanism devised to explain Uranus’ tipped axis trips over the normality of the Uranian moons.

If there’s little or no core in Uranus (it’s the second least dense of the planets, Saturn’s the least dense) it’s at least possible that a slow migration of the planet’s axis, analogous to a spinning top, and due to an irregularly shaped rocky core (or a split core, that is, *two* rocky cores), may account for the change in the axial tilt without screwing too much with the moons. And of course, we’re only seeing the moons now — if they’re ejections or captures by Uranus, the migration of the Uranian axis may have been what normalized them to their current state.

Van Flandern’s EPH might be looked upon as one explanatory model, except for the fact that there’s no explanation for the explanation. :’)

http://www.universetoday.com/18879/density-of-uranus/
http://nssdc.gsfc.nasa.gov/planetary/factsheet/uranusfact.html

http://www.universetoday.com/21618/density-of-neptune/
http://nssdc.gsfc.nasa.gov/planetary/factsheet/neptunefact.html

http://www.universetoday.com/15322/density-of-saturn/
http://nssdc.gsfc.nasa.gov/planetary/factsheet/saturnfact.html

http://www.universetoday.com/15116/density-of-jupiter/
http://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html

The other model (which I’d posted before, somewhere, maybe on FR) for the axial tip is the arrival, from the direction of one of the original poles, of the mass of liquid that makes up most of Uranus today; the previous mass of the planet might have been smaller, currently (it sez here) it is about 14 1/2 times the mass of Earth; its original density would have been higher. Arrival of this mass would have to have been sufficient to change the axis after some period of instability.

...or...

The arriving mass might have been what is now the rocky core, or (you guessed it) the secondary rocky core, producing the irregular mass distribution which has altered the axis of rotation until it’s nearly in the ecliptic. This is a bit cleaner, and more probable than the arrival of a long train of water of at planetary mass probably exceeding the mass of the Earth.