Hello Vangulik
I had similar problems with my .223 remington chambered S&W MP15I. Some bullets, especially 62gr Barnaul got stuck to the rifling when chambered. No problems when shooting, but similar problems what you have had occured when extracting live cartridge from the chamber. "Pogo sticking" like Gamma762 instructed was always needed. Or "mortaring" as I have used to call it.
The problem with pogo sticking or mortaring is, that if the bullet is too tight stuck to the rifling, the procedure might leave the bullet to the rifling and extract the unfired case and spill the powder all around your receiver. No harm done, but you need to clean the rifle and use the cleaning rod to tap out the stuck bullet.
There's one simple test you can do to examine, if the bullet takes the rifling contact when chambered. 1) Take black marker 2) Take cartridge and paint the bullet black 3) Chamber the cartridge 4) Extract the cartridge 5) Examine the painted bullet for possible signs (scrapes or scratches) for rifling contact.
Tight chambers have better accuracy potential, but those might be picky with various cartridges.