We find that suspicious - are there any services that allow us to do a background check without asking the landlord's permission?

Always easier to ask for forgiveness then permission.

@Alex Smith I'm going to assume that your lease states that the tenant can not do any work on the property without your permission.

If you do not meet the selection criteria, or if you provide inaccurate or incomplete information, your application may be rejected and your application fee will not be refunded.”Landlords running a credit check on prospective tenants as part of the application process must meet several conditions, including: (1) The landlord must get the prospective tenant’s written permission to run the check. (2) If the landlord declines to rent to the tenant based on the applicant’s credit report, the landlord must inform the applicant of this in a “Notice of Adverse Action.”

Right now, I'm listening to Seth Godin's "Permission Marketing."

Had the loan been with our after tax money, it would be a no brainer.Our question is, is this a permissible transaction?

Sure, you can find them on google, but if you use them without permission, you are technically breaking the law. 

I don't need their permission.

You will have to be on the phone with them on a three way call with their lender, and they have to give verbal permission to the bank to talk to you on that phone call.

As I started marketing the property, I received numerous rental applications, many of which are from individuals with Section 8 vouchers.After doing some research, I learned that it's not permissible to reject applicants solely based on their possession of a Section 8 voucher.