Thank you Michele, ( ignoring the spell check driven typo of "think" for "thick" (-: ). We should be able to put this "thin" discussion behind us.
The "thin" discussion should have taken about 2 email exchanges. Here is CIRA's (thin) search for .ca domain names [disclosure: it is my domain name]
 
Domain name: artisanalpot.ca
Domain status: registered
Creation date: 2016/12/14
Expiry date: 2017/12/14
Updated date: 2016/12/19
DNSSEC: Unsigned
Registrar:
Name: Web Hosting Canada (7081936 Canada Inc.)
Number: 5000080
Name servers:
ns1.whc.ca 173.209.49.178
ns2.whc.ca 198.245.53.176
ns3.whc.ca 198.245.61.86
% WHOIS look-up made at 2017-01-25 11:32:24 (GMT)
% Use of CIRA's WHOIS service is governed by the Terms of Use in its Legal
% Notice, available at http://www.cira.ca/legal-notice/?lang=en
% (c) 2017 Canadian Internet Registration Authority, (http://www.cira.ca/)

Nothing private is disclosed and LEA would have to resort to legal means to get to what is in the "thick" data set.
There are no ICANN policy  issues here.

Sam L <artisanalpot.ca> (-: