If we go through an rental agency or agent is there some sort of disclosure of that information that is required

If you use an agency, you can ask them to verify that info for you. If they don't then you don't have to sign the rental agreement, and they don't get the commission. You sound like a great tenant and financially stable landlords would be happy to have you. Finding good tenants is just as hard (or more so) than finding a good house to rent. Even, if you rent directly from a landlord, you can ask them about their loan/equity situation. If they run a credit check on you, you could just as easily run a credit check on them. All they can do is say no.