It was inevitable that Fox would get this wrong and it's also inevitable that the rest of the mainstream media will follow their lead,but for the record, Hillary was not booed because she said she supports the troops --- she was booed because she blamed the Iraqi government for the failure of the occupation --- a commonly used line among Democrats as well as some Republicans despite it's rather loathesome implications.
I assume the Democrats have focus grouped this line and find that it appeals on some level --- and I think you can all imagine what level that might be. (It could be argued that it's a tactic to force the Iraqi government to make some moves before the election if they feel that the Democrats are going to be harder on them...) But the fact is that horrible cock-up in Iraq is the result of a foolish and cynical US invasion invasion of Iraq and a complete lack of any intelligent planning for the aftermath. To blame the Iraqi government for the intractable sectarian differences that most respectable experts and historians predicted would make this deluded neocon project a failure is pretty cheap.
The progressives gathered at the TBA conference are not uninformed or likely to misunderstand the unpleasant implications of this approach and so are a very poor audience on which to use it. Nonetheless, Fox News and others who are making this into something else as a way to tar the candidates and liberals again with lack of patriotism are asses.