I can confirm that this is still the case. The Flash Player Download page still offers only the out-of-date version, even though the Flash Player Help page tells you you're out of date and need to update, both it and the Advisory link to the Flash Player Download page with 197 offered, not 213.
The distribution page was updated last week to the latest version, 126.96.36.199. If you're not seeing the latest version, either with the text on the page, or the installer files themselves, please private message me the URL you use to download the files from and include your geo-location.
I'm getting the latest version 213 now,