The way I heard it, English Heritage are not denying that they moved the stones during the past hundered years, beacuse it's quite obvious that they did. It's just that not a lot of people know that.
If you look at the painting William Turner made of the site in the late 19th century, you'll see that it was far more jumbled and collapsed than it is now, with many stones looking as if they will fall over. Many of these have since been cemented upright, and some of the blocks have been placed back on top of others. Most of this work was done in the 1920's, around the time it stopped being privately owned. The problem now is that people are starting to suspect that they might have got it wrong...
In response to the whole place being a hoax, that's fairly unlikely. It seems to have first been recorded in the 12th century, according to stonepages.com (who also have some rather nice photos):
Early mention of Stonehenge was made in 1135 by chronicler Geoffrey of Monmouth, who claimed that it was brought by a tribe of giants from Africa to Ireland, and from there flown by the wizard Merlin across the sea. Another legend claims that the stones were stolen from an Irish woman by the Devil, and re-erected on Salisbury Plain by Merlin for Ambrosius Aurelianus, the King of Britons.
The area has some earthworks dating back to about 9000-8000 BC, and the stones are belived to have been erected from about 2100 BC onwards.