Reality television is a genre of television programming that documents purportedly unscripted real-life situations, often starring unknown individuals rather than professional actors.
Factual television is a genre of non-fiction television programming that documents actual events and people.
Scripted reality [...] is a subgenre of reality television with some or all of the contents being scripted or pre-arranged by the production company.
It is pretty clear that scripted reality and factual television are mutually exclusive - a show cannot be both at the same time. An example for factual television is Highway Patrol, an example for scripted reality is Lenßen & Partner.
Is there any show / series / movie which belongs to the genre "reality tv", but is neither factual nor scripted?