Firefox does auto-download an OpenH264 binary on systems without a supported H.264 decoder library (if this feature is enabled, which it isn't currently in Debian's iceweasel packages). But note that OpenH264 is free software available under the BSD license:

https://github.com/cisco/openh264/

Firefox downloads binaries from Cisco because Cisco can legally distribute this software in binary form in countries where H.264 patents apply, while Mozilla can't do so directly.

There was also a plan discussed to make it easy to automatically verify that the binary corresponds with the published source code, but as far as I know that work hasn't been done yet:

https://github.com/cisco/openh264/issues/893

Also, if you have the correct gstreamer H.264 plugin installed, Firefox should use that instead of downloading OpenH264.