It is false. The Pan-American Highway doesn't completely connects the Mexican-US border with Chile, because it has an interrupted sector of 130 km between Colombia and Panama.
Its 48,000 km of roads will eventually connect North America with Chile when this section is completed.
The remarkable stretch that prevents the road from fully connecting is a journey of approximately 130 km of hard mountainous jungle, located between the eastern end of Panama and the northwest of Colombia called the Darien Gap. The Pan-American Highway is cut in Yaviza (Panama), and in Lomas Aisladas (Colombia) the Pan-American Highway in South America begins again.