I wonder how those who repeat this is not the OP's problem and call this request for help cheeky will feel if they ever end up old and alone with health problems.
It isn't about whose "responsibility" this is, it is about an older lady in need and doing what you can to help.
Accompanying her to an appointment does not equal becoming a carer, it's just a bit of kindness.
Also if you really are too busy to go to hospital with her on those days, which is perfectly valid, it is quite possible to still help and show kindness.
Saying because she has been on the planet almost 80 years she should therefore should know about navigating the world is just wrong.
Using the internet could be on many varying levels and does not prove she can do everything.
The people who visit her may be unable or unwilling to help too. Who knows?
The world has changed so much, is still changing everyday. By the time you are mid seventies there will probably be things you can't cope with unaided. Many older people are being shut out of society by increasing technology.
You could suggest hospital transport or a local voluntary car scheme and help her find the contact details.
This would take minimal time from you but could make a lot of difference.
Christ, some people have so little empathy and just see older people as an inconvenience.
Living on your own as you age and become ill or disabled is hard enough without the attitude of some people.