Let's take a look at what happens, and folks can decide for themselves the "danger" involved.
First, it is not recoil as such that sets of a primer. If there are, say, two rounds in the tubular magazine, recoil does not "drive" the bullet point of the rear round into the primer of the front round.
What happens is that when the rifle recoils, both rounds, obeying Mr. Newton, try to stay where they are. So they move forward in relation to the gun, compressing the magazine spring. When the recoil force ends, the magazine spring reasserts itself and both rounds slam backwards to the cartridge stop. Since this also leaves the rear round in a free position, it tends to center itself, so its bullet point is not at the bottom of the tube, but in the center, right where the primer of the first round will strike it.
So that sort of thing can only happen if there is enough room for the cartridges to move far enough to create the needed momentum for firing the primer. Obviously, one round in the magazine is no problem, nor is a full magazine. The danger comes when there are two or more cartridges used out of a full magazine, leaving at least two rounds. (The Remington 14/141 pump rifles have grooves in the magazine tube specifically to slow a moving round down enough that its momentum is not enough to fire its primer if it hits a bullet point. Winchester never did that because its rimmed rounds lay at more of an angle and did not present as much of a problem as Remington's rimless cartridges. But magazine grooves or not, Remington warned against use of pointed bullets.)
There is another problem that has occurred with some shapes of flat nose bullet. In this case, the scenario is the same, except that the round is straight cased (e.g. .45 Colt) and the bullet has a flat, but sharp edged nose. Under the same circumstances, the sharp edge digs into the primer, which is usually a soft pistol primer, and the round lets go.
So quite a few things have to happen just the right (or wrong) way, at just the right time, for anything to happen. And what is the result if it does? The answer is, not much. The cartridge will burst, but the thin magazine tube does not allow enough pressure buildup to cause a lot of damage. In tests, the tube splitor bulged, and sometimes the forearm split. Shooters to whom it has happened reported a blow to the hand, but no serious injury.
Still, the rifle was damaged, and the shooter could have been injured. So it is still good advice to avoid use of pointed bullets in tubular magazine rifles.
Jim