I have been setting up some blogs here on WordPress.com over the last few days and I had the same trouble you are having with getting remote images to "green check" by loading from a URL.
The images I wanted to load are from my own private server -- so I knew the images were alive and working elsewhere -- and while I have .htaccess hotlink protection, the WordPress.com blog URLs were included as approved remote images pullers.
Here's where it gets strange: While the images would "Red X" under Firefox for Mac, they would load just fine in the WordPress.com editor using Safari for Mac and Google Chrome for Mac.
So, I did a lot of testing, and it came down to me having to turn OFF "Always use HTTPS when visiting administration pages" in "Browser Connection" in "Personal Settings" here on WordPress.com.
After I removed the HTTPS connection, and cleared my cache and closed Firefox -- I was able to get the "Green Check" loading remote images via URL under Firefox.
If you aren't using HTTPS -- then I'm not sure how to help you, because I tried everything else... turning off Flashblocker and Adblock Plus and a whole host of other features in Firefox and WordPress.com and on my private server... and it was WordPress.com HTTPS that was causing Firefox to choke.