I would hesitate to take the situation described to you as gospel. People have a way of oversimplifying to try to make their situation more effective. It's quite possible that the other reasons were valid, and possibly one of them involved the amount of medical leave available.
While an employee cannot be fired because they need a transplant, if FMLA applies the employer is only required to provide up to 12 weeks of medical leave (unless state law or legally binding contract, policy or CBA specifically says otherwise). Once the twelve weeks has expired, the employer is legally entitled to terminate the employee and hire someone who is able to be there and do the work. The law has to balance the right of the employee to keep their job when they are ill, with the right of the employer to keep his business operating. This applies no matter how legitimate the need for additional medical leave, with the caveats already mentioned.
FMLA applies when all of the following are true: (1) The employee has worked for the employee for 12 months or more (2) The employer has a minimum of 50 employees within 75 miles of the employee's location (3) the employee has worked no less than 1,250 hours in the 12 months immediately preceding the leave and (4) The employee or a qualified beneficiary has a serious health condition as defined by the statute. If even one of the 4 criteria is not met, FMLA does not apply.
If FMLA does not apply, then the employer only has to provide the amount of medical leave his policy provides for. Additionally, FMLA does not protect the employee from being fired for reasons that are unrelated to the leave. If they would have been fired whether they took leave or not, then FMLA does not prohibit the employer from firing them anyway.
It would by no means be the first time I have heard, "I was fired for being sick" when, in fact, the employer had held the employee's job open for the statutory time and only fired them when they were unable to return to work after the appropriate time expired.
