It is possible to travel through a nether portal without standing inside the portal. As long as any part of your hitbox aligns with the portal's interior, you can teleport because the game counts the edge of your hitbox flush with the nether portal blocks as proper collision. This is true for all entities. Watch the attached video clip to see what I mean.

It is not just the bottom, but the sides and top as well.

To reproduce: Build a nether portal. Walk right up to the bottom of the portal and touch it. You should teleport.