Sure, if you think jobs are defined by height. Batum is taller and lankier, so he's the 3.
But if you think jobs are defined by natural inclination, talent, and pay scale, Batum makes more sense at SG. Batum has the talent to be a pretty effective offensive player, taking guys off the dribble more, taking midrange jumpers, using his passing skills. But he needs the ball in his hands to do that. Next year he's going to be paid like a key member of the offense, so we might as well use him that way.
Matthews, in contrast, really doesn't have any driving or passing ability. He's a much better candidate to be "that corner guy." And given his past, he probably feels lucky just to be in the NBA. So being a defensive role player is probably not a big deal for him.
Batum (20%) and Matthews (18%) had similar usage rates last season. They both took about 11 shots per game (although Batum hit at 45% while Wes hit at 41%). They were used kind of interchangeably. I think if Batum were posting here, he'd say, "Look, this has to change. Wes is a nice guy and a hard worker. But he doesn't have my tools, he isn't being paid my kind of money, he's two years older and nobody talk about 'upside' anymore when you talk about Wes. It's time to tip the balance in the offensive sets so I get more shots and more possessions. I get a little more of the Brandon Roy Awesome Shooting Guard treatment, and Wes gets a little more of the Role Playing SF Standing in the Corner treatment."
I suppose you could throw out the whole "SG/SF" thing, since in the real world lots of SF's play the "featured offensive player" role. But when I hear Batum say he wants to play SG, I interpret that as him saying he grew up on the Blazers playing next to Brandon Roy, and he thinks he can be more of that guy.