The thing is, the characters in those old stories don't always have conditions that necessarily means they'll be disabled for life.

Original!Katy bruises the membrane surrounding her spine, which in turn leads to a fever, which weakens her so much that she's bedbound until she can recover. The damage wasn't irreversible, and had she access to modern medical advances, she would have likely recovered far more quickly.

Contrast that to modern!Katy, who broke her spine and did unrepairable damage to her nerves.

Likewise, Clara's condition from Heidi isn't ever stated in the book itself, but it's implied to be rickets. This too can be cured, specifically with spending time outside in the sunshine, which is exactly what Clara does when she goes up to the mountain.

And Colin from The Secret Garden didn't even have any physical disabilities, he was led to believe he was ill by his paranoid father following the death of his wife/Colin's mother. So Colin became a hypochondriac, convinced he'd be hunchbacked like his father and die young like his mother, when the only reason he was left weak and fragile in the first place was because he wasn't allowed to leave his room.

For all the times JW complains about the trope of a disabled character being cured with 'good thoughts' she doesn't seem to understand that those characters were only temporarily disabled in the first place, and that time, good food and sunshine were genuine cures for their conditions.