I think it may be even simpler than you think. I have the achievement but i'm not very good online or play much online racing.
I'm not 100% sure if this works but i played Outbreak in a Jam Session against only one person and never actually won the whole session (i.e. highest score after the five rounds), but i won the round when i was the first infected and "tagged" the other player, this means i got +2 and the other got zero giving a round score of 10 point to me and 8 to the other player - giving me a Round win, I think these wins count.