I do have to address the issue of must in past contexts,
and not just in "reported" or "indirect" speech. Must
in its senses of either strong obligation or of strong probability is
not only acceptable, it's usual in dependent clauses after verbs like
told, knew, felt, realized, etc., in the past (notice
that the verbs are not just verbs of speech). Even Otto Jespersen, in
Essentials of English Grammar (1933), recognizes this usage,
She said she must be back by seven.
He knew suddenly who the woman must be.
Below are some of the many instances of the past uses of must
in dependent clauses that I found by looking in the COBUILD corpus,
using simply "that he must" as the query phrase. You can see that it's
I realized that he must be the man who produced
.left Taylor facing problems that he must solve.
.rejected the suggestion that he must choose between
.chairman wisely reminded him that he must either
ask a question or be quiet.
It's pretty futile to tell learners that must should
be changed to had to in all past contexts. Like Mr.
James Yeh, who asked the original question, learners will find must
used frequently in past contexts. It's more realistic to advise them
to use had to in past tense independent
clauses, and to use must in dependent
clauses (usually noun or adjective clauses) when the sense
is that of strong obligation or strong probability.