What you point out is important here. There is a lot of confusion about the difference between ESA's (Emotional Support Animals) and Service animals. The latter falls under FHA and ADA laws, and landlords must be extremely careful about how they handle these requests. My partner and I run a blog about issues independent landlords and property managers face, and we've written a couple articles about this:
landlordgurus.com/emotional-support-animal-housing-laws/
landlordgurus.com/should-i-accept-pets-in-my-rental/
An important consideration is whether to accept pets, both because doing so strategically can increase rental income and because it can head off tenants' temptation to manipulate ESA laws in order to get pet into a rental that doesn't otherwise allow them. I fully concur that petscreening.com is a valuable resource!
A few disclosures - we may make a commission on some of the products we talk about on our site, and we are NOT lawyers! This latter point is important because our content, like any others like it, cannot be substituted for careful consideration of ESA and Service animal laws. Rental laws are constantly changing, there are local differences, and it is NOT worth risking a costly lawsuit. We recommend consulting a lawyer when there is any doubt about landlord-tenant laws.
Thanks! Eli