Further testing reveals that popup windows need to be enabled for the FA site for the Setup => Attachments View button functionality to work. The Sales => Add?Manage Customers => Attachments View Attachment button works okay even without such settings.
This is so because, the former uses a "button" tag whilst the latter uses the "a href" tag.
# Setup => Attachments (needs popup exception for FA domain)
# Sales => Add/Manage Customer => Attachments (no need for pop settings)
The HTML code inspection reveals the Concerned Lines:
# Lines 199 and 227 in admin/attachments.php
<td><button type="submit" class="editbutton" name="view3" value="1" title="View">
<img src="../themes/default/images/view.gif"
style="vertical-align:middle;width:12px;height:12px;border:0;">
</button>
</td>
# Line 95 in includes/ui/attachments.inc
<td style="text-align: center;">
<a target="_blank" class="viewlink"
href="../../admin/attachments.php?vw=3"
onclick="javascript:openWindow(this.href,this.target); return false;"
accesskey="V">
<img src="../../themes/default/images/view.gif"
style="vertical-align:middle;width:12px;height:12px;border:0;">
</a>
</td>