Yes in the old MW2 we knew, Ghost got shot by Shepard. but in the MW2 reboot, the betrayal does happen where Shepherd turns his back on Ghost. But he doesn't die in this timeline. It's just like MW 2024.

44 Magnum. Ghost is last seen being thrown into a ditch along with Roach. Although the player only sees Roach being covered in gasoline and set on fire, Ghost is undoubtedly lit on fire along with him (the soldiers would not have left unless they were sure they both were dead).