Saying that someone has died when nobody has really died seems to me like a big lie! And it seems so unnecessary! She didn't even need to give a reason, just that she was not working on that day.
I'm afraid to me that would tell me that the person, therapist or not, is a bit unstable. Why resort to an outlandish lie in order to do a perfectly ordinary thing and take a few days off?

I find it hard to trust and so I get very upset if it seems to me that my T has contradicted himself or changed his mind on something. It has led to some arguments between us and a lot of upset for me, in the past. But we have always worked it out and it has usually been about T being careless and/or a misunderstanding between us, never a really serious lie.