Jack Black, who appears as a drug-addicted star of coarse comedies attempting to broaden his range, admits he was surprised Stiller's film has been criticised for its treatment of the disabled.
"I thought, if anything, Robert would get the heat mostly because what he does seems to be the most sensitive taboo," he told the BBC News website.
Downey Jr (right) plays an actor who has had his skin artificially pigmented
"You're not supposed to portray characters of that particular tone," he continued.
"I guess you never know where sensitivity will crop up."
As far as the star of Kung Fu Panda is concerned, however, Tropic Thunder's satirical script "makes fun of the whole world".
"I think we were pretty equal opportunity," he said, adding he hoped audiences would "cut us some slack".
That certainly seems to be the case in North America, where the film topped the US box office chart for three weeks and has so far made more than $100m (£56m).
Part of its appeal might be down to seeing Tom Cruise in the atypical role of a balding, paunchy and foul-mouthed movie producer.
"I think it was just a fun thing for him to do," reveals Stiller. "He was really able to let loose."
For Jack Black, however, it was the notion of satirising Hollywood's excesses that made the project irresistible.
Protesters took to the streets outside Tropic Thunder's US premiere
"What made this appealing was the chance to make fun of the movie industry," he said. "Ben and his friends got it right on the money.
"What I loved about the script was that it was so irreverent and fearless," he continued.
"The bravery of some of the jokes was what made me laugh the hardest."
"Making movies is a crazy world sometimes," said Stiller, who claims that the film's outlandish plot - which involves a group of actors who get caught up in a real conflict while shooting a war movie - is "all based on reality".
He did admit, though, that the specifics had been "maybe tweaked a little bit."
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