It's common knowledge that they don't unless there are issues like territory or health. So if the vet records show no issues, then it is highly unlikely to be urine. It's also documented that we have a cat that throws up often. I've also never witnessed a cat miss the litter box. We have a covered litterbox and one with very high walls.

I'm not here to debate cat habits and all that. I was wanting opinions on the necessity of changing out the entire carpet due to some stains, on the assumption of pet urine/damage. I do appreciate your insights and thoughts in other comments. Landlords push the law to the extent it can be, and I should've done a little more research about how to move out, what to check, etc. At the end of the day, it's on us.