Actually I got it in the e-newspaper. If I relate the idiom on that context then it means "Any person or institution is an independent on paper but in reality it is puppet.

I have already read it but i did not get as much to use the word in another place. Thank you sir

No sir it is an idiom

Were they, at the time, referring to a coloulful bird in a cage?

I don't think it is a common idiom in English anywhere as google only found the one instance of "like a caged parrot". However it might be something that someone would make up spontaneously as a colourful uncomplimentary expression.