When taking damage Minecraft calculates the angle at which you are attacked. This is stored in the player's data at attackedAtYaw. The server has this data but the client doesn't receive this data so the camera doesn't tilt in the direction attacked and just defaults in the tilting to the left. This broke in 1.3 due to singleplayer worlds now internally using a multiplayer server.
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We're tracking this issue as MC-26678, so this ticket is being resolved and linked as a duplicate.
That ticket has already been resolved as Won't Fix, which means this is considered a bug but won't be fixed. The description of that ticket or the comments might explain the rationale. Please do not leave a comment on the linked ticket.
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