Feels like a noob question, but..

PerBonomi - 

1. user?? - it is checking for the object is available or not. For the anonymous user, an object is available. 

2.  user.id?? - it is checking for the user.id key available or not. Even for the anonymous user, this key is available. 

3. user.login != "" - It is checking if user.login is not blank, however, for anonymous user user.login is being returned as anonymous.

Solution: 

if you want to check for an anonymous user you can use below code. 

<#if user.anonymous>
</#if>

OR

<#if !user.registered>
</#if>

OR

<#if user.id != -1>
</#if>