I really like the idea of using a version control system on media files, but I can see some of the limitations it would bring to the table. If that option is truly out of the question, my go to solution for media storage is a CDN (content distribution network), for the following reasons:
First, it is accessible (nearly) everywhere. No pesky authenticated network issues, or VPN for that matter. The files can be searched, secured, or a GUI (typically web-based) can be built to display all of the media in lists or preview form, depending on the CDN you choose. AWS Security Example.
The number of people that actually need access to the raw media (psd, ai, pdf, mov, mp4) files for editing purposes is likely less than the number of people that might want to use the subsequently generated media (png, jpg, pdf, webm, ogg). The number of people that understand the corporate style and brand guidelines is also most likely limited to the team of people that need access to the raw files, so those can be stored in a different location on the CDN.
Want version control? You can have that too with some CDN solutions. AWS S3 Versioning. They also, typically, have access logs which can be invaluable.
If a hosted solution is not in your budget, there are open source CDN solutions available. Though the cost of CDN hosting is extremely affordable compared to the time and cost associated with having to manage a CDN server. MaxCDN Pricing, AWS Pricing
Last, but not least. Storing your media on a CDN makes updating files in production environments (for web) as easy as dropping in a new file of the same name and the file is replaced. Branding for internal documentation is also a breeze for web-generated PDFs which would also be accessing the CDN for media references. The "last mile" so-to-speak, would be Microsoft Office flat documents, but this will be the same problem with almost every solution. They will need to be manually updated. Until you ditch them and use PDFs for everything that will be distributed.
Chances are good that if your company has a web presence, it has (or should have) a CDN anyway. If two birds with one stone sounds like a win, I'd say look into it further. I have tried to provide more than just Amazon Web Services links, but it is what I use and what I'm familiar with. My perspective is slightly skewed, but I wouldn't hesitate to suggest looking at as many options as you can before deciding on any solution.