A white list can be given to any TER member (non-provider) at any time. The recipient doesn't even need to request it.  There's been cases of white lists being given to people who never saw that provider.    
   
 P411 OKs, however, must be requested.  And as part of the request, you need to give details on the date of the session and other details to help the provider remember you.    
   
 Maybe these differences are why some providers don't give white lists much value for screening, while they may more readily accept P411 OKs, based on what I've seen in earlier threads on this subject.