Why oversample if you already satisfy Nyquist rate?

[DragonPetter]

I am told that if I want to get phase information from a signal, I should oversample the signal well beyond the nyquist rate.

I am confused about why this is suggested, since I thought the nyquist rate was the minimum frequency needed to avoid aliasing. I understand building in some safety space, but why is it necessary to go well beyond this rate?

 

[DragonPetter]

Sorry, I found a good explanation here
http://en.wikipedia.org/wiki/Oversampling

Don't know how to remove the question here.