There's plenty of precedent; a number of successful American sitcoms, including All in the Family, Sanford and Son, and The Office, are Americanized remakes of British shows (though I don't know to what extent the same actual stories were used).
From what I understand, the 1st season of the American
Office is pretty much a total rehash of the British version. After that, the American version really struck out in its own direction.
There are a few other British series that were remade in the U.S.
Cosby (the later CBS series, not NBC's
The Cosby Show) was an American remake of
One Foot in the Grave. NBC attempted unsuccessful American remakes of
Coupling &
Red Dwarf. Coupling mostly just reused the old British scripts and only lasted 11 episodes, only 4 of which were aired.
Red Dwarf went through a few different iterations but never made it past the pilot stage and was never aired on TV, although you can find it on Youtube. (While it's generally acknowledged that the American
Red Dwarf was crap, nearly all of its actors would later go on to better things. In fact, the American versions of Cat & Holly were played by Terry Farrell & Jane Leeves, who immediately went on to play Jadzia Dax on
Star Trek: Deep Space 9 & Daphne Moon on
Frasier, respectively.)
Before the show even premiered everyone came out and said they would be using old USA scripts and just fixing them up a little to make some sense in the UK.
I guess most don't notice.
Well, it's not like the old Ben Stone episodes get as much rerun time anyway.
The one thing that bums me out about the recycling of old
Law & Order scripts for the new British version is that it makes it that much more awkward to do a proper crossover story later.