Problem/Motivation

I notice that the permission "view signatures" is not checked anywhere in the code base in 6.x-1.5 or current 6.x-1.x-dev.

The original method of restricting who can view signatures is the field "Display Mode:" with the setting "Do not display signatures to the public". Since this is at the bottom of the Advanced Petiton Settings fieldset, and the default value is "Normal display", people overlooked this setting. This is also confusing semantics, because maybe the administrator wants to set a particular display setting, but not allow the public to see the display. Can't do both with this field.

6.x-2.x adds a new field at the top of the Advanced Petition Settings fieldset that is a checkbox: "Hide signature tab".

So, to recap, there is an unchecked permission "view signatures", and then two separate settings per petition that also affect access.

As a result, the function petition_signature_access is checking four separate conditions to make a decision about whether to show the signatures:
$node->display_mode == Do not display signatures to the public
user_access('edit own petition') and (user created petition)
hide_signatures_tab checkbox
node_access 'view' permission

So that's 16 possible permutations of settings that an administrator can be confused by.

Proposed resolution

Ideally, think the patch would be to delete the "Display Mode: Do not display signatures to the public" choice from being displayed.
For legacy installs, it would be easiest to keep checking this setting rather than try to update the database.
Delete the "view signatures" permission, to avoid confusing people, or actually check it for those who need the ability to grant role based access.

Use the new "hide signatures" checkbox as the primary way to make that setting.

I would offer a patch, but I think the maintainer needs to decide how to resolve.

Cross references to related issue:
Do not display signature count as a link when user doesn't have access
Signature tab displays even when user doesn't have permissions