Checking the credit of the tenant is about the landlord worrying they won't get paid. This is entirely unrelated to the tenant's relationship with a potential subletter.
The rest of your post stands, though - landlords have a valid concern for the condition of the apartment, disruption of other tenants, &c.
As a - former - landlord, I can tell you that I was interested in much more than just credit scores. I wanted to have stable, long term tenants in my units. I also wanted responsible people who would tell me if there was a drip so that I could fix it before it became and issue. I found that the more time I spent vetting tenants, the less time I had to spend worrying about disputes and other issues. Tenants live in a valuable asset and everything from their cleanliness to job stability really matters.
Right, my point was that the parent had mentioned credit scores, and those in particular were irrelevant. As I said, the general point - that landlords deserve some measure of oversight in the handling of their valuable assets - absolutely stands.
The rest of your post stands, though - landlords have a valid concern for the condition of the apartment, disruption of other tenants, &c.