The issue isn't just pressure, but the area over which that pressure operates. The .223 has a small internal case diameter, the .30-30 is mid-sized, while the 6.5 is virtually the same as a .30-06. Multiply the internal cross-sectional area of each case by their chamber pressure and you get the force trying to stretch the frame. Very rough examples:
.223- .101 sq.in. x 55,000 psi = 5555 pounds of force.
6.5 - .126 sq.in. x 51,000 psi = 6426 pounds of force.
The Swede applies about 16% more force, enough to potentially cause damage to the frame. And the Swede is not a low-pressure cartridge in all loadings. Norma factory ammo produced 51,000 psi in Accurate Arms' pressure barrel.