My personal headcanon for TF2 is that there is no other team.
Redmond and Blutarch just happened to hire the same 9 people and they just keep switching colors because as long as it's a stalemate they all keep making money.
One side always wins though because they have one extra person.
The multiple versions of the same class that you see in the Meet the Team videos (Like the entire army of Soldiers) is merely CGI and costumed actors hired by the director (the one who gets killed by Pauling) to punch up the videos.