Permissions issue related to anonymous users

Below you can find two screenshots. Next to every post we have the comment bubbles.

When I'm logged in with the admin account I can see fine all the bubbles. (screenshot1)

When with anonymous user and/or authenticated user, I can see only the bubble for the first in the list page/blog and apart from that it doesn't even link to the correct page/blog but to another one. (screenshot2)

Source from the bubble html when doing view-source with anonymous:

<li class="comment-comments"><a href="/?q=node/1#comments" title="Jump to the first comment of this posting." property="sioc:num_replies" content="1" datatype="xsd:integer" rel="">1 comment</a></li>

I found out that by giving anonymous access to "Administer blocks" and "Use contextual links", then it works. (Only with the 2 of them combined) Anonymous users are able to see the bubbles then.

I tried a fresh installation of Drupal without any contrib modules installed, the issue remains.

Can I do something from my side to help on this? I tried with devel but I haven't used it before and couldn't find anything. In the recent logs of Drupal I don't see any warnings.