It's funny (not haha funny, obviously) because Jemma tries so hard to project this bravely suffering saint-like image, but the reality is that illness often just brings out all the worst qualities that some people already had, precisely because being ill makes them untouchable. It's pretty obvious from multiple comments that she (and Clive) were always greedy, grasping, insincere people.
Jemma's illness just made it possible for her to go on the beg in a massive way, with the bonus that anyone asking questions immediately gets shut down by her latest sob story, even though she regularly shows herself living a more active life than plenty of healthy people do. I don't doubt that she's ill, but there is so much about her story that is just deeply weird and inconsistent.