(Put another way: the right of publicity will limit commercial use of Instagram photos, at least in the states that recognize it. But TMZ is editorial use, not commercial use.)
http://www.apug.org/forums/forum137/82809-legalities-relatin...
After 20 minutes of searching with Google and reading on about 10 websites I couldn't find any photog sites that even reference the law ...
According to Wikipedia[1]:
"Publishing an identifiable photo of a person without a model release signed by that person can result in civil liability for whoever publishes the photograph."
1) Usually it does not make sense to sue amateur photographer.
2) It may make sense to sue Instagram and their clients, especially when serious money are involved.
IANAL
Granted, I'm not an Instagram user so I could be entirely wrong but the network effects of Instagram don't seem to be strong enough to push their users around too much.
It's far more likely to be something less damaging but more obvious to users, like in-feed advertising.