On Being Old and on your own.

I am 73 and my wife is 66. My sons and daughters are living at different locations, quite away from me. I and my wife live in our house at Indore. Some people, including my children, think that it is not wise to live by ourselves because we are old and may need help (medical, etc.) any time. Still we do not want to lose our freedom and our independence by becoming dependent on others. We continue to live on our own. Am I right? Please advise.