Dogs are about 99% oriented around scent. Perhaps changing the angle of their two nostrils allows for a more accurate 3-D perception of their world? Asked to fetch a named toy, the dog "reads" the room in olfactory stereo to locate the object for retrieval.
It's not particularly good science to assume the universe is limited to what humans are good at perceiving. I'm sure there are some potential publications in this somewhere.
I wouldn’t think the difference in distance between the two nostrils would make it possible to differentiate smells spatially. You need some amount of separation between the inputs for a “3D view”. And both sides of the nose are ultimately connected into one nasal passage. I’m not sure where all of a dogs olfactory receptors are, but that wouldn’t help much either.
Moving the head around (from side to side) would make more sense to establish the direction of a scent. Then the strength could tell the dog the appropriate distance a smell is away too.
But if the head tilt was about trying to get a better perception of the world from a smell point of view, they wouldn’t be so consistent in their head tilts. The article said that dogs tend to tilt their heads in only one direction (left or right). And that the direction was always consistent for that individual dog. If they were trying to map out smells in 3D space, they’d move their heads around in more varied patterns.
That said, I do think your larger point of not assuming dogs (or any animals) have the same perception of the world as we do is correct. For example, we would identify a toy based almost entirely on how it looks. But a dog would definitely also take into account how it smelled. The same theory of "concentration" to explain the head tilt would be valid, regardless of what the dog is trying to remember -- look or smell.
It's not particularly good science to assume the universe is limited to what humans are good at perceiving. I'm sure there are some potential publications in this somewhere.