I tend to use my cross draw rig always - especially when mounted but don’t understand the armorer’s comment that pulling the pistol from a cross is (more) dangerous - maybe it’s a little more dangerous for the horse as he’d be in a more direct line of getting hit in the neck with an unplanned discharge.
Not only are you performing a 90 degree sweep(know your target and beyond), you are also using more muscle groups to get the gun on target. Definitely more dangerous.
Can people perform it safely? Sure, those that practice and aren't bumbling old know-it-all actors. I still wouldn't want to be in that sweep arc which is why most ranges do not allow cross draw holsters. Outside in single use "pits" with berms all around, no issue.
That statement is well understood in the Firearms training industry. To remove a gun from a cross draw holster almost always involves sweeping or lasering some part of your body or other directions around you other that the ground and down range towards the target.
Most shooting schools will not allow cross draw or behind the back holsters for training for this reason.
Now cross draw for single action cowboy shooting may be viewed differently, and I am not into cowboy shooting (yet). But for defensive shooting with most defensive pistols (not single action), cross draw is not encouraged.
If you are facing the general direction of he target, the gun barrel will cross about 90 degrees on its way to he target. If you discharge prematurely,... well you get he idea. Anyway, probably an important consideration on a movie set.
Cross draw = Too easy to sweep.