The genuineness (or otherwise) of the sickness doesn't come into it. It's the number of absence events and their individual lengths that drives this. Under your employment contract, you are offering to work for your employer and you get something in exchange (a salary package). If an individual keeps being unavailable for work - for whatever reason - the employer may use the disciplinary process to investigate your absence and set a plan with you to improve it. A period of monitoring then occurs. if the individual fails to hit the plan, the disciplinery process then may be escalated. Eventually the individual can be (fairly) dismissed on the grounds of capability. In other words the individual is not capable of delivering to the employment contract.
Individual circumstances mean that each case must be taken on its own merits - but an employer must unsure a fair process, and set a reasonable plan.
If you are genuinely ill, then you cannot work. But that doesn't change the fact that it is impacting your capability to do your work.