The Builder's Tape Measure (which you'll find in Inventory > Library > Objects > Household) agrees that 2.8m is the proper height for a door opening in Second Life.
All this seems perfectly fine in Mouse Look, just like how I see things iRL. That's the way it is supposed to work, right? So the camera position is what makes the difference. Here's a comparison of the normal Second Life view to one where the Camera Controls were used to adjust the pitch so that the camera was as the avatar's eye level.
None of this explains why the books on his shelves look far to big, too.