Okay, whipping that dead horse a bit longer, let's look at your points favoring double rifle over bolt for dangerous game.
1) Double rifles are supposed to be heavier with less muzzle jump. Most of the double rifles I observe in videos have very short barrels, presumably to cut weight. They also appear to have considerably less wood, especially in the fore end, also presumably to cut weight. Most don't wear scopes which also = < weight. They only carry two vs four or five cartridges and that can be a not insignificant weight reduction. And lastly, though the double rifle action is shorter, I suspect the weight difference is not significantly different (extra hammers and springs = heavy bolt assembly). My 404J Mauser weighs nearly 11 lbs loaded with scope and sling. How does a stubby DGR double compare? I'm also finding it hard to believe a short barreled much larger caliber double rifle would have significantly less muzzle jump than my 24" barrel much longer action 404 Mauser. But maybe I'm wrong.
2) Speed of a second shot. You presume this is always an advantage. I can easily argue that it certainly often times is very much a disadvantage, especially if the shooter accidentally fires both barrels simultaneously or before the gun has settled on target from recoil. I have yet to see a video of double fire in a field situation but I'm sure a few are out there. I have seen several where the shooter (client or PH) fired the second barrel too quickly and badly missed the animal. Sure, a bolt hunter can also miss the second shot, but he's still got two more for correction if time allows. And reloading a bolt action on the run is a lot handier than a double rifle. By the way, I did shoot an incoming gemsbuck twice through the heart with my bolt action Springfield at <30 yards and then running by at 12 yards. And she was running plenty fast and I do not reload on the shoulder. I remount the rifle after cycling. Gemsbuck are not officially "dangerous game" but they are nonetheless plenty dangerous. My outfitter had a close call dispatching a wounded one two years earlier. And they are not afraid to scrap with lions. For an experienced hunter a bolt action can be fired quite fast.
3) Are double guns more reliable? If the first barrel fails to fire, would the hunter go ahead and take the shot at a dangerous animal knowing he doesn't have a followup barrel? And if the second barrel fails to fire during a charge, the hunter is no less screwed than the bolt guy who's gun somehow collapsed after the first wounding shot. This is all tinfoil hat conjecture. Probability of failure is obscure for either gun. Clearly double rifles have more mechanisms than bolt actions. More mechanism would seem to favor more probability of failure.
4) And some more conjecture. Wounded dangerous game do not always run off and hide, giving the double gun guy time to reload. From what I'm seeing on the videos, this is rarely the case with elephant. At any rate, my experience has been I can put two rounds into a charging animal at less than thirty yards very accurately with a bolt action rifle. Presumably Harry Selby and Wally Johnson were also capable since they preferred to stop wounded dangerous game with bolt rifles.