From OP's post I get the impression that the decision to offload the sick passenger was considered a misdiagnosis. In cases like this the question to be decided isn't whether the passenger is healthy but whether there is need to see a doctor ASAP.

OP's reaction to the situation seems strange to me, most normal people would have asked for hotel recommendations and called to the insurance company instead of buying new tickets... In situations like this continuing the trip when not advised by doctor, could cause serious insurance problems both for the airline & OP.