False, as Panama gained their independence from Colombia, not from Mexico.
In 1903, the U.S. instigated a rebellion in the Colombian province of Panama by inciting nationalists to seek independence. The U.S. promoted this rebellion to ensure a favorable deal from the newly independent Panama for the Panama Canal, which the U.S. had desired for some time but which had met with resistance from the Colombian government.
After the rebellion, the U.S. struck a deal with Panama for ownership of the territory surrounding this new canal, territory it held until 1999.
The United States came to the colonization game rather late. By the time of the presidency of William McKinley, the world had already been carved up by European powers. With a strong desire to prove itself as the equal to Britain and France, the US closed out the 19th Century by engaging in a war with Spain that took from her the last of her colonies.
Today the United States has long since given up its hopes of becoming a colonial empire, but it still holds on to many pieces of its early 20th Century attempt to become one. The story of the US Territories is one of the least known and most interesting parts of American history.
Here's everything you need to know about the territories of the United States from Everything-everywhere.com.