Final answer:
Panama indeed revolted and gained independence because Colombia refused America's offer for the canal's construction, and this led to the signing of the Hay-Bunau-Varilla Treaty which allowed the U.S. to build the Panama Canal.
Step-by-step explanation:
The statement is true: Panama successfully revolted against Colombia when Colombia refused America's offer for the canal's construction. Colombia deemed President Roosevelt's offer for the Panama Canal construction insufficient in terms of financial compensation.
In response to Colombia's hesitance and higher demand for payment, Roosevelt clandestinely supported the Panamanian revolution. U.S. military intervention prevented Colombia from suppressing the revolt and facilitated Panamanian independence.
Afterward, the newly independent Panama quickly agreed to the terms of the canal's construction with the United States. The Hay-Bunau-Varilla Treaty was signed, granting the U.S. the right to build and control the canal zone. While the canal itself became a marvel of engineering and a boost for trade, Roosevelt's actions sparked controversy and had long-term implications in U.S.-Latin American relations.