If one agrees to your statement this would mean except these few 'paid media' houses, rest of the TV channels and news papers fall into 'free media' category or charity enterprises.
Could you share what is the definition of the paid media and unpaid/free media applied by you to categorise them as per your post. .
Having worked in media for some time here is my learning, there are 3 terms you can identify media under, with definitions and examples below:
1) Free media- this is what ideal media working should be but is hard to find as media is run by humans not robots who do have some soft corner. If you would want me to think of one media house in India I can vouch for being free and fair then I believe I cant take any name but if you would want me to take journalists name then there are a lot of names you can yourself follow
2) Influenced media- these are media people who are easily influenced but by not directly paying. Corproates are known for taking media junkets on tours on excuse of product launches to get favourable reviews- and these exist all across the board
3) Paid media- they do exist and these are called advertorials, Times of India is known to start this trend and if can pay you can buy any space on Times of India. Having said that, the responsibility of content lies with you.
4) Sponsored Media- This is where Niti Central type of organizations lie, they work on an agenda and should be least trusted as they present half picture