Sylvia remains silent and doesn't speak because she doesn't want to betray the loyalty of the white heron. When the handsome hunter, who manages to charm Sylvia, asks her where the beautiful bird might be hiding, Sylvia decides to remain silent and not give away its location. She realizes that, even though the hunter was probably the closest friend she ever had, the white heron is actually more important to her, as it represents the nature that she loves and admires deeply. By remaining silent, Sylvia basically saves the white heron's life:

Sylvia cannot speak; she cannot tell the heron's secret and give its life away.

In this case, Sylvia's silence is more powerful than denial because it represents her resoluteness, her determination, her loyalty, and perhaps even her sense of justice, and it shows us where her heart truly lies.