32-vs-64-bit flash player download confusion

I'm running 64-bit W7.  When I visit http://get.adobe.com/flashplayer/, it correctly identifies my OS and browser (

Your system: Windows 64-bit , English, Firefox), but when I click "Download now" it gives me what appears to be the 32-bit version of the plugin (http://aihdownload.adobe.com/bin/live/install_flashplayer11x32_mssd_aih.exe).  Shouldn't it be sending me to http://aihdownload.adobe.com/bin/live/install_flashplayer11x64_mssd_aih.exe?

Thanks in advance for any clarification.