I prepared 3 video formats for my site:
/assets/video/background-purple.ogg
/assets/video/background-purple.webm
/assets/video/background-purple.mp4
Seems I've found a solution:
I switched my ogv codec from VP8 to Theora and now Firefox can play video correctly.
I used this code for the source:
The MIMEtype is:
AddType video/ogg .ogv .ogg
And the codec is:
Xiph.org's Theora Video (theo)
I guess it could work also for .webm but I've not tested it.