Yes, the case is often re-decided by people who were
not there originally to hear the witnesses' testimony.
The witnesses' testimony is seldom *relevant* to appeal.
Trial cases rarely get overturned on questions of
facts (eg, what witnesses testify about). For precisely the reason you describe - the appeal judges haven't seen the witnesses - courts tend to be reluctant to overturn a finding of fact at the trial level, and the threshold to do so is very high (things like "the judge's decision on facts has to be entirely unreasonable".
Trial cases get overturned in the overwhelming majority of cases on questions of
law - that is, questions that are about interpreting and applying the law, about the rights of the involved parties and so forth. The witnesses and evidence are pointedly irrelevant to deciding what the law actually says and means, so there is no reason whatsoever to assume those who heard the witnesses' testimony are more qualified. Trial judges have no particular qualification over appeal judges for interpreting the law, and juries have particular *dis*qualifications on the question - legal illiteracy is almost a requirement of jury duty).
So casting doubts on appeal courts on the basis that they don't see the witnesses is a bit of an empty talking point.