Hi Ashley,
Given that you had to roll-back, your site is as it was before, that is, it is a Moodle 2.6 installation. Then, if there is a problem now, it just means that the problem existed before the update but maybe no one noticed or... something else changed during that process, which actually lead to the current problem. In other words, the problem could reside somewhere else and not in Moodle itself.
I just went to the site, so you could have another point of view, and just as Emma, I saw the said image fine (at the News forum).
***
I made a few tests at the Moodle demo site and images, whether they were embedded at the post (pluginfile.php?file=/31/mod_forum/post/etc) or added as attachments (pluginfile.php?file=/31/mod_forum/attachment/), always are downloaded if one browses to their URL. So this behaviour is normal, as far as Moode is concerned. Why? Well, that I don't know. Just to confirm and be actually sure about this, I did the test, 1) at the front page news forum, 2) at a course news forum and 3) at a course normal forum. Also, enabling (pluginfile.php/38/mod_forum/) or disabling (pluginfile.php?file=/38/mod_forum/) Slash arguments (administration > Server > HTTP) didn't change anything.
When images were placed anywhere else (e.g. in a course topic label), browsing to their URL resulted in them being displayed as expected, that is, they were not downloaded automatically. As far as this issue is concerned, apart from asking a Moodle developer about it, I don't think it can be considered a bug.
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Regarding the "but then it says the file is damaged, corrupt or too large to open" situation you mentioned, each and every image (enet-pba.png, pba-m1.png, Using_Cell_Phones.jpg, orient.gif, intelinfo.png & the Moodle logo) I downloaded from your sites (yes, plural), downloaded fine and I could see them in my computer without any issues.
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Now, I said "sites" because you have two Moodle installations interacting (and yes, they are different installations, it is not a domain redirection):
- http://online.enetlearning.org/ (the one we went to check the front page image).
- http://onlinelearning.enetcolorado.org/ (the one referenced or sent to after selecting a course).
So, I started at the first site and clicked the "here" link to preview courses:
http://online.enetlearning.org/ **1**
click here to PREVIEW OUR COURSES:
that took me to the second site:
Home > Courses > eNetLearning Preview Courses
http://onlinelearning.enetcolorado.org/course/index.php?categoryid=26 **2**
there I selected the "Preview - Intel Teach Elements: Project-Based Approaches" course:
Preview - Intel Teach Elements: Project-Based Approaches
http://onlinelearning.enetcolorado.org/course/view.php?id=7 **2**
in there I opend the topic 0 banner image:
banner topic 0
h--p://onlinelearning.enetcolorado.org/pluginfile.php/1435/course/section/44/enet-pba.png **2**
and the topic 2 banner image:
banner topic 2
h--p://onlinelearning.enetcolorado.org/pluginfile.php/1435/course/section/46/pba-m1.png **2**
both opened and displayed fine (no download, no issues)
Back at the course list page I selected the "Preview - Using Cell Phones as Learning Tools in the Classroom" course:
Preview - Using Cell Phones as Learning Tools in the Classroom
http://onlinelearning.enetcolorado.org/course/view.php?id=6 **2**
same thing, opened both a banner and an icon (at a third site) without issues:
banner topic 0
h--p://onlinelearning.enetcolorado.org/pluginfile.php/1414/course/section/36/Using_Cell_Phones.jpg **2**
icon topic 1
h--p://courses.edtechleaders.org/workshops/workshops_img/orient.gif **3**
Back at the front page, the news forum image was downloaded after trying to browse to its URL (just as it happened in the tests at the Moodle 2.7 demo site):
Announcements from eNet Colorado
h--p://online.enetlearning.org/pluginfile.php?file=/19/mod_forum/post/32/intelinfo.png **1**
I also opened and displayed the Moodle logo in a new tab without problems:
Moodle logo
http://online.enetlearning.org/theme/image.php?theme=clean&component=core&rev=1401306384&image=moodlelogo **1**
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Conclusions:
1. Automatic downloading of forum images seems to be the normal action.
2. Images from different places could be downloaded and displayed without problems.
3. Given that we have been able to see and download the images at your site, without any issues, my thinking is that the problem could be at your own computer. You could start by doing a thorough virus--malware--browser settings--browser plugins check. Just as an extra reference for you, my environment is: Windows XP (32 bit) and a Chrome based browser (SRWare Iron).
4. The error you got from your navigating "directly" to the pluginsfile.php script is normal and it just indicates that that is not how that script is to be used; in other words, the error message lets you know that the script expects one or more arguments.
So... given that everything points, not to Moodle itself, but to your own local environment, you should seriously get someone to help you check your computer. Then you could check if there is an actual need to have these two installations interconnected. I guess you need to have a good talk with your client's IT area.
Hope this helps.
Cheers! 
--- edited
I just had to edit this post (change "http" to "h--p") to avoid having the image links referenced displaying the images instead of the links... like so:
