That is likely your issue. If the main game is on Steam, so does the DLC need to be purchased from / used on. If you purchased the DLC from GOG, its not usable with the Steam main game.
Sorry for the confusion. I own the main game on both platforms. I purchased it again when it came out on GOG to support y'all and then bought the DLC for the game there as well.
However, if I try to play with the GOG copy (full game + all DLC) with a friend who has the Steam version, I get the error previously mentioned. There is at least one other person experiencing the same issue on the GOG support forum.
EDIT: According to Patokai on the GOG forum, he solved the problem by copying over the Steam version of the "Sins of a Solar Empire Rebellion.exe" to his GOG copy. Is this a recommended workaround?