Thank whatever television gods there be, that has not been the case, at least so far. John Barrowman's character Jack Harkness has been left absolutely alone, and while I find it helps to know his background, you can watch the series without having seen any of the previous Torchwood series. Most of the main characters were killed off in "Torchwood: Children of Earth", but the scriptwriters managed to work all the major survivors and a few minor ones into the current plot-line, so it feels a bit like coming home. I'm not sure about any of the newly introduced characters yet, but since the initial episode was only an hour long the writers haven't had a lot of time to spend on character development yet.
A bigger worry than the show being "Americanized" was that there was no way they would be able to top the plot-line of "Children of Earth". I needn't have been concerned. Just like CoE, Miracle Day has taken a lightly used concept and taken it to fresh grounds. Without giving any major spoilers (all this becomes known in the first few minutes of the show) on "Miracle Day", death literally takes a holiday. The first show leaves us with characters who are in a state of confusion about what is happening, but shows us that what sounds like a miraculous gift is actually a terrible curse. One of the established minor characters who has been brought back does some quick math and figures out that this means that the Earth is gaining 1.5 million people a day, and that food, potable water and other supplies are going to run out within a few months. Somewhat later in the program it is established that it is impossible to die; regardless of the damage done to the body the mind remains aware.
These little snippets of information are provided in the first half of the show, but the first episode mostly involves itself in how the key characters are finally gathered in one place. The first hour ends in a way I should have seen coming, but didn't. I will definitely be taping the remaining episodes.