I know what you mean, OP.
Long time ago, when I worked in the NHS, we employed a Lab Assistant. She was a small woman in her 40s or 50s, and she was told exactly what the work involved, including lifting things. She said nothing about having a long term back complaint at this point, nor did she say that she wouldn't be able to lift heavy things, which would probably have resulted in her not being suitable for the post.
So she got the job, and within a month had "hurt her back" (she may well have done!) because she was lifting heavy things that she couldn't manage, despite there being plenty of people around whom she could have asked for help, rather than struggle.
She went off long-term sick after being employed for a month and we never saw her again; BUT that whole time, we couldn't employ anyone else to do her job either, in a very busy lab, that had really needed that extra member of staff.
As I say, she may well have genuinely hurt her back - but she knew that was a risk, she knew that lifting was part of the job and she took it knowing that she might end up hurting herself and going off sick. That's what made us cross, the seeming deliberateness of her actions.
And it does happen in private companies too - last year, DH had a sales manager who apparently had cancer. We say apparently because it was never determined what sort or where, he had treatment that seemed sporadic, he never produced doctor's notes, would just miss work days (some of which happily coincided with school holidays). DH was working with HR to try and decide what to do, the man was due a disciplinary for something bad that he'd done, so he resigned on the grounds of ill health before HR insisted on seeing medical corroboration of his illness.
Next thing DH knows, he's getting a request for a reference from the company that this man has just got a job with - suggesting that he wasn't as ill as he was making out.
The worst of that scenario was that DH's direct boss had died at the beginning of the year of liver cancer; and he'd worked right through, only taking days off for the treatment, but never missing more than he had to.
This other man never even looked ill after the treatment, but in reality it was the lack of detail and the lack of medical corroboration that made everyone doubt it was real.