It's not what you believe, it's what the facts show.  The issue is whether there are two dwelling units here, or just one.  The fact that there are separate entrances, points to two.  But was there still access from basement to upstairs?  Was it used?  Did the owner use any of the upstairs for storage or occasional events or other purposes?  Pub 523 depends for authority on the Regulations.  You might want to review Examples 3, 4 and 5 under (e)(4), starting at Page 14 here:

https://home.treasury.gov/system/files/136/archive-documents/po37162.pdf