It's the other way around: people with immotile cilia have 50% situs inversus (because it randomizes the body orientation). When Kartagener first identified the connection between sinuses and situs inversus, he didn't know to look specifically for cilia. Sinusitis by itself is pretty common, so the syndrome was originally identified by this combination of symptoms. So, by the original definition, 100% of Kartagener patients had situs inversus. When immotile sperm was discovered as another symptom of the same condition, it became clear that there's an equal, previously unidentified pool of Kartagener syndrome patients with sinusitis, bronchitis, and immotile sperm, but with normal organ configuration, so the definition of the disease changed to reflect that — it is also now known by a different name, primary ciliary dyskinesia (PCD). Situs inversus can also happen due to other mutations affecting the process of side assignment, not necessarily having to do with PCD. PCD is just the most common out of several causes of situs inversus.
So is this true, that people born with situs inversus are those random 50% of embryos with immotile cilia?
It's the other way around: people with immotile cilia have 50% situs inversus (because it randomizes the body orientation). When Kartagener first identified the connection between sinuses and situs inversus, he didn't know to look specifically for cilia. Sinusitis by itself is pretty common, so the syndrome was originally identified by this combination of symptoms. So, by the original definition, 100% of Kartagener patients had situs inversus. When immotile sperm was discovered as another symptom of the same condition, it became clear that there's an equal, previously unidentified pool of Kartagener syndrome patients with sinusitis, bronchitis, and immotile sperm, but with normal organ configuration, so the definition of the disease changed to reflect that — it is also now known by a different name, primary ciliary dyskinesia (PCD). Situs inversus can also happen due to other mutations affecting the process of side assignment, not necessarily having to do with PCD. PCD is just the most common out of several causes of situs inversus.