In the Japanese version of DPPt it straight up says humans and Pokemon used to get married all the time. In Colosseum there is a woman who straight up says that her life-long boyfriend is her Mightyena. In Pokemon Special, there's the "A Shocking Case of Poke-Love: 'That's the last time I'll ever take a bath with my Tentacool'" article in a newspaper during the RBG arc. In one episode of the Best Wishes anime, it's shown in a fantasy a man and a Gothitelle getting married. There's other evidence through the series of such things, as well.
Who's to believe romance between Trainers and Pokemon is not somewhat common or at least accepted in the Pokemon world? Most media definitely show Pokemon as having at least near human-like sapience, even if they can't speak human languages to express it that easily, so that general idea that they're just animals is out the window.
So, what if they did more with this sentiment somehow? Go more in-depth with how close some folk get with their Pokemon.
In the English DPPt it's still hinted at that marriage was a thing. "They dined together" is the line they use here, suggesting that people and pokemon were family. In my own headcanon, this was mostly the case until the kid with the sword went on his murdering rampage, and since then Pokeballs became the only way to really communicate with Pokemon.
<3 Lilligant fo' life.
Official Gardevoir of the Pokemon X Message Boards