In India does it matter whether you get insured with a public or private insurance company?

I think still many people would consider it safer to get insured with a public insurance company(like LIC or United India Insurance Co.) rather than with a private one because rejection rate in the case of former is much lower than in the later case. I have also read one report published in a magazine which supports this. What is your opinion?
Do you know about any website where this issue is discussed in detail? I would like to read more about it.

Thanks for you suggestions.

Do I need a PAN card to avoid deduction from my salary if I have a Business Visa?

I came to India for an internship, and got a Business Visa.

In the company where I’m working they say they have to deduct from my salary(stipend) since I don’t have a PAN card.

I know some other interns (foreigners) in India, who are also on business visa, without a PAN card, and their company doesn’t need to deduct from their salary(stipend).

Please provide the details of the regulations regarding this matter.
Thank you.