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:
<source src="/assets/video/background-purple.ogv" type="video/ogg">
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.