It's not that hard, actually. 99% of DNA is the same, but how the DNA is arranged is pretty unique per species.
Except that they aren't doing full genome sequencing (which is vastly more complicated and vastly more expensive). They are sequencing only specific regions of the genome. It would be similar to comparing the Bible to the Koran based on how many times they use the word "Thou". In the end you'll know they're both books and they're different but you won't know the chapter counts or the year of publication.
Surely a basic DNA test would at least check the number of chromosomes matches up.
Not necessarily, and for more than one reason.
- One, it's a different test (genotyping vs karyotyping)
- Two, chromosomes aren't all that stable against shipping and storage (and hence could be degraded by the time they arrive)
It's why certain genetic diseases in humans can't be found in dogs exactly - the DNA that is problematic would exist in a different chromosome on a dog.
That doesn't apply here though. Sequencing technologies are not biased towards or against particular chromosomes, and the chromosomes are not sorted out before sequencing. The whole sample goes in and primers bind to anything they have affinity to. Sequencing then proceeds regardless of whether it starts on chromosome 4, 16, 21, or some other chromosome entirely - as long as the start and end are on the same chromosome. And if you're looking at variable regions within genes, the likelihood of those starting and ending on the same chromosome is exceptionally high.
CBC Marketplace did such a test nearly a year ago... and yes, they even submitted human DNA as well. Quite a few of the tested companies did detect it as "non dog DNA".
Which may just mean that the other company had included some additional tests to look for "non dog DNA", and this company did not. That's a smart control that this company should have thought of, although depending on the scenario it might only tell you about contamination, not complete substitution.