Well, no. The tight leade does not raise pressures significantly. What does is something not mentioned, which is the thicker brass of GI loads. Look at the picture above but further back, at the case neck. That neck must fit into the space for it in the chamber.
Now about the first thing that happens when the powder charge is ignited is that the high pressure gas forces itself into the case neck and expands it, leaving the bullet floating, for an instant, in a stream of gas*, held back by its own inertia.
Then the pressure builds and the bullet moves into the leade and into the rifling. At that point, the leade doesn't impose much impediment to the bullet; under that kind of pressure the bullet becomes almost plastic, like silly putty, and will conform itself to the shape of the leade and rifling.
But, if the chamber neck is too tight, or the case neck brass is too thick, the case neck cannot expand and pressures rise.** Both the chamber neck and the case neck are made with specifications, a figure of xxx +/- dimensions. So if a SAAMI chamber is cut by an old reamer and so is of minimal size, and the cartridge was made with brass of maximum thickness or with a case neck diameter of the maximum size, the case neck cannot expand and there can be trouble.
*It is that gas, flowing past the stationary bullet, that causes throat erosion, but that is another subject for another time.
**That is why the Germans, converting the old M1888 rifle to use the new ammunition with a larger bullet, needed only to expand the chamber neck; they didn't rebore or re-rifle the barrel.
Jim