Interesting question. I did a bit of research, and didn't find any definitve answers. But the wikipedia has a nice section on "Domain name system". The first thing I found was opinion that the privacy isn't worth it becuase bygodaddy gave any the informaiton too easly.
Regardless, basically the registrar is required to collect informaiton on you for them to set up the contract between you and ICANN. Providing false informaiton can loose you the domain. by that it would seem that you still own the domain is yours, even though WHOIS info doesn't show it as such.
There have been court ruling that declair domans as property (see sex.com vs. Verisign article at wiki pedia) And the reinforces the idea that the domain is yours regardless of the publicaly aviable informaiton.
I only wonder what whould happen if a registrar went out of business, or decided they didn't want to release a domain for transfer - how much harder is it going to be to get your domain back, since the records that prove it's yours arn't publicaly avilable?