You can definitely believe all that he has claimed. The media generally loves to portray him as a deranged loser and won't pass up any chance to mock him. They paint a picture of Govinda being approached by Cameron on the sets of Bhagam Bhaag . And Govinda refused and the role ended up with Sam Worthington.
If you check the dates and history of Avatar's production schedule, everything he said makes sense.
You can google for Avatar's earliest script written by Cameron in 1995.It was originally called Project 880. This script was significantly different than the 2009 film version. The protagonist wasn't even named Jake Scully. Project 880 was to be Cameron's follow upto Titanic with a planned 1999 - 2000 release.
This was the version actually offered to Govinda. He was one of the most successful Indian stars in the late 90s to early 2000s. He likely declined it as had several hindi films already in various stages of production. Cameron too later shelved the project as if felt that the technology to can this film wasn't upto his expectations.
Now regarding Govinda mentioning that he would have had to paint his body blue for 400 days. It may sound preposterous at first. But you only need to have a general understanding of the history of cgi and motion capture on film.
The first succesful or popular mocap character that looked very convincing was Golem from Lotr: Fellowship of the ring and its sequels directed by Peter Jackson. This was the first character to have facial expressions and acting mapped onto a cgi character. Jackson soon made King Kong in 2005 with the lead character mocapped by Andy Serkis.
It was after watching this 2005 King Kong film, that Cameron decided that it was time to revive and shoot Avatar with this new technology.And thus we got the 2009 version of Avatar.
The script and characters went for a rehaul and one would naturally wonder how Govinda would have fitted into the role of a US soldier.
Remember that Cameron had offered Govinda the role 8 years before the release of the final film. There was no motion capture back then and paint and makeup would have been the way to go. Like the Planet of the Apes film of Tim Burton that was released in early 2001.
Now about Govinda suggesting the title of Avatar to Cameron after listening to the story. That is also likely because the film was titled Project 880 for a very long time. He had changed the title to Avatar only in 2005.
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