IMO Third Watch is no more a remake of Emergency than Hill Street Blues is a remake of Adam-12.
I agree, and I'm sure the people who actually created Emergency and Adam-12 would agree. And that's
actually what matters and underlies the whole "remake" distinction. If the producers of a new program could "get away" with making that program (not some other) without paying the creators of some previous program, I suspect today's ROI-conscious society would have them do so. So whether to make something as a "remake" or not is defined by the law (along with the long-standing principles of the writers' discipline to which the law often defers), by the principles that determine when one production lends so much of its foundation from another that the creator of the earlier production is entitled to assert their ownership interest in the new production.
It isn't a matter of whether fans
feel the new production is so different
, but much more so a matter of whether the creator
of the old production has rights, by law, due to how the new production is so similar