It's true. To be specific, the flower falls in one entire bulb (like a severed head) at a time, instead of a few petals at a time like Sakura or Sazanka, which is a close relative to Tsubaki.
It looks a bit grim to some people, not exclusively to samurai. It's quite clear that almost no samurai family use this flower as a family insignia though.
I'm not so sure about the word being used as a euphemism for bad luck (even by samurai) though :)
It is an incredibly beautiful flower, representing some great human qualities that Japanese people treasure. It's planted in temples and shrines, and used as given name to girls.
It's frequently used to portray sad moments in movies, but probably not at all associated with bad luck by normal people in daily life.
Another meaning
I researched a little about this word and I think there may be a fourth meaning to it, which is 'Samurai's bad luck', because of the way that the camellia all falls off at the same time. I am not sure if this is true and would love to hear about it more. Thanks! :)