I don't know about other languages on this but in English media or medium also has the sense of what environment someone or something is in. "What's your medium" "I use oils" etc. I suppose that it comes from the Latin, but can't find that dictionary at this time. I can find the Esperanto English dictionary which says that medio means "Sphere of (action, life) environment, social circumstances, habitat (surroundings)" etc. I don't know if this helps, but I really don't think that it's such a stretch to make the connection as one may think.
/redakto: ŝajnas, ke en la Rusa, pola, ĉeĥa kaj bulgara estas parenca vorto.