I cannot add images to post/pages via Add Media button

Hello WPMU,

I cannot add images to post/pages via Add Media button.

So far, we've tried:
- Clearing the cache
- Switching browsers
- Switching machines
- Switching networks
- Trying it from a different city
- Trying different user accounts
- Switching themes
- Disabling plugins
- Increase server resources
- host not blocking any IP
- addons in broswer disabled
- no firewall on PC

Nothing has helped.

The strange part is that no one from support(not olny WPMU) cannot comfirm this issue.
Only one of WPEngine techs was able to replicate it once but nobody else was.

Could you point me to right direction or give me a clue of what else could be done here?