My opinion is that Burke and Owen did love Cristina

I was sad that Burke left Cristina but the narrarive tried to say he did it because he loved her.

And I do think Owen loved Cristina because he never really moved on while she was around and was a great friend to her in season 10 and she seemed to value that.

That might seem contradictory but we probably have to understand the context that Burke's actor had to leave the show so there wasn't the option of Burke staying around after things went wrong like Owen.