I've never thought that Anne was not ill or that it was secretly Lady Catherine's fault, for many reasons, but mainly because Jane Austen tends to be very clear when someone is a hypochondriac. There are a ton of them in Austen's novels and the narrator always makes a snide remark or just informs us outright:

Mrs. Bennet: When she was discontented, she fancied herself nervous (at this time that meant a disorder of the nervous system, not "anxious)

Mr. Woodhouse: The evil of the actual disparity in their ages (and Mr. Woodhouse had not married early) was much increased by his constitution and habits; for having been a valetudinarian all his life, without activity of mind or body, he was a much older man in ways than in years (noun: a person who is unduly anxious about their health.)

Mary Musgrove: While well, and happy, and properly attended to, she had great good humour and excellent spirits; but any indisposition sunk her completely. She had no resources for solitude; and inheriting a considerable share of the Elliot self-importance, was very prone to add to every other distress that of fancying herself neglected and ill-used. (and the following conversation with Anne quickly reveals that she is exaggerating her illness for attention and can't even keep track of what times she was "ill")

Lady Bertram: From about the time of her entering the family, Lady Bertram, in consequence of a little ill-health, and a great deal of indolence, gave up the house in town, which she had been used to occupy every spring, and remained wholly in the country

I could probably go on, especially in the fragment of Sanditon. Now yes, Jane Austen may have been ignoring mental health problems that she couldn't have known about, but it's pretty clear she thinks these people are being silly. But not for Anne de Bourgh, I cannot find this sort of remark about "fancying" or anything. Instead, we have Maria and Elizabeth shocked at how small and sickly Anne looks"

"Only look at her. She is quite a little creature. Who would have thought she could be so thin and small!” (Maria Lucas)

Miss de Bourgh was pale and sickly: her features, though not plain, were insignificant; and she spoke very little, except in a low voice... (Elizabeth)

It seems to be a modern reading to think Anne isn't ill, probably because we just don't really have "sickly" people anymore. (edit formatting)