This thread happened three years ago, but this is the top response that came up on a google search for "sorry this type of video cannot be saved to this device".
I signed in to Apple just to comment. The guy responding to this question, Diesel vdub, is legitimately the least helpful commenter I've ever seen. How this person has a Level 7 next to his name is beyond comprehension.
"Nothing can be added to CameraRoll unless is taken with the device."
"I was able to save videos from my Dropbox to my phone before."
"Ah, I missed that part."
What was there to miss? You were wrong with your previous statement.
"iOS 7.1 has not been released. As such, it cannot be discussed here."
"Discussion of beta software in the public forums is a violation of the developers agreement which you signed/agreed to." Who are you? You're distracting from your incompetence and toward an issue that's not an issue. "I'm sorry, I can't fix your engine because your washer fluid is too new."
Thankfully there are other sites to go to for this issue.