Plain physics. The screen is 800x240. The paralax barrier is diverting the vertical lines 1,3,5,7 etc to the left, 2,4,6,8 etc to the right. In 3D the system renders two images at 400x240 each. In 2D the full 800x240 is used on one framebuffer.
The paralax barrier is always visible in 3D, when the power is turned off, the light passes straight through, instead of aiming left/right respectively. If they would show the same picture on lines 1,3,5,7 as on lines 2,4,6,8 you would get a stretched image
1-2-3-4-5-6-7-8
a-a-b-b-c-c-d-d
This is physically impossible.
^ This is how a 3DS game looks resolutiion-wise in both 2D and 3D, 3D just adds... 3D, but doesn't "increase PPI" in any way. If anything some people say games look jaggi-er in 3D.
The perceived PPI, it's not adding more pixels to the display of course. The PPI is at it's highest in 2D as you can actually see a single image in 800x240 as opposed to 3D which is 400x240 per eye. (which obviously looks jaggier)