But then, my wife's parents are definitely not well-off (unlikely to ever retire) and they still sent us small "just because" gifts occasionally when we were young and poor.
And I literally don't know anyone with a kid and a non-terrible (not even necessarily good) relationship with their parents who hasn't received a lot of free child care. Parents -- even those who have to work hard to make ends meet -- find time for the grandchildren.
So if the definition was "any amount of cash/any service for a reason other than birthday/holiday", then I kind of have to agree with your parent.
So I definitely agree that having parents who can work and take occasionally vacation and have any amount of disposable income is definitely a huge blessing. But I don't think it's particularly rare in the US, either.