To be consistent with the actual value that gets submitted at the configuration page in the Users module:

<input id="users_config_reg_uniemail_yes" type="radio" name="reg_uniemail" value="1" checked="checked">

Also, elsewhere in the API code, there was inconsistencies in how the value was being checked. (Sometimes it was only checking if the value was "1", instead of checking for TRUE as a bool. Nevertheless, it was better to check against via the values "1" and "0", since those are the values being stored.