True.
> The American progressive movement co-opted the word "liberalism".
No, they didn't. For quite some time, the American left [0] (called "liberal" dominantly for some decades, some adopted the moniker "progressive" when it was perceived that the right had created bad associations with "liberal" a few decades ago, but with very little in common, in terms of ideas, with the older progressive movement, either in terms of substantive ideology, policy preference, or contemporary relative left-right position), right (usually called "conservative"), and libertarian political camps have all been dominated by, or at least significantly shaped by, ideas that trace back, in different ways, to 18th century liberalism and its struggles against 18th century conservatives. And all three have adherents who claim that their group is the proper heir to classical liberalism.
[0] relatively speaking, before anyone makes the common argument that by international standards, the US has virtually no left, with the major parties ranging from center-right (Democrats) to far right (Republicans).