I shoot doubles a lot - SxS shotguns much more than rifles - and I have fired many thousands of rounds through them. I always fire right (front) first unless I am firing the second barrel for a reason - i.e tighter choked first shot. I have never had a double fire both barrels because of firing the forward trigger first, and then accidentally hitting the second. Have had a pre-war Merkel shotgun do it, but it was a worn seer, nothing to do with hitting the second trigger. It would be very difficult for me to learn to instinctively use a different manual of arms for a double rifle - and I am pretty sure the British gunmakers assumed their clients would use their rifles like their guns.
In fairness, I should also add, that my heaviest recoiling double trigger rifle is a .470. My 500/416 is single trigger, and the 9.3 x 74R’s aren’t real recoil generators. I do have a double ten-bore that with full loads will cause one’s eyes to water a bit, but again, it hasn’t doubled on me.
As Phil notes, this comes up periodically, and I wonder what the cause is. It obviously happens to some shooters, occasionally to others, and never to most. Another issue is the trigger guard pounding the second finger. Again, I have been lucky, but know others who have to put the little recoil shields on their trigger guards. It may be as simple as finger/hand length or as complicated as trigger hand technique - Phil, I am not accusing you of having short fat fingers, but ......