Hi, joshieboyo!
You seem just as capable as looking after yourself as my nan can, well, more so, as she can't even work her house phone half of the time! Bless her!
If any of us were to suggest that she go in a home we'd never hear the end of it. She only has the use of one eye and has recently been diagnosed with diabetes, but manages fine. She does fall occasionally, but that's more to do with her eye and the fact she rushes around everywhere! I go 'round everyday to help her test her blood sugar levels, but she's my nan, not a burden.
I think your son is, maybe, suggesting it so, as you say, he'd feel he'd done all he could for you if anything were to happen. You know what you're capable of, stick to your guns!
You're as old as you feel, as they say! :o)