Stone was mobbed by press members and angry protesters as he arrived for a screening of controversial film South of The Border in Santa Monica, California.
Alonso took the chance to confront Stone outside the screening, but the director was seen waving off the actress when given the chance to debate.
The Venezuelan-raised Vampire's Kiss star has previously blasted the director for his "considerable prowess to crafting a cinematic lie".
She explained to WENN: "Why not tell the truth about the conditions in Venezuela, where the middle class has shrunk from a third to five per cent, kidnapping has risen to the top five in the world and murder rates are higher than in Baghdad resulting from pillaged oil wealth, increased drug running and exportation of political unrest?"
Meanwhile, Alonso plans to continue protests challenging Stone's portrayal of Venezuela under the Chavez government. The actress narrates new movie, Crossing Our Borders, which chronicles what she claims the director left out in South of The Border.