If the tenants don't trust you, you can say that you have deed to prove your ownership. Since it's a public info, you can also advise the tenants to check out at County's recorders' office.
In the most cases like this, there is no deal made if there is no trust between the tenants and landlord.Very likely, the tenants are not very serious about your property. They are either trying to find some execuses or over cautious. They could be very picky as well.
