No, the tribal members do own the land, its just unlikely that a bank could ever foreclose because of the tribes involvement and how tribal land works. Non-tribal members get leases. The federal land rules are archaic and work against the tribal members.

Have some of the wealthier tribes fixed this problem for themselves? If they can't create a tribally-funded financial arrangement that makes a bank happy, couldn't the tribe just do the lending?

Of course, not every tribe has a casino, but if those that do had innovated in this area, we'd have a better idea of the best direction for federal funding.

Even tribes with casinos aren't rich[1][2], and yes the tribes that have cash generally give enough to their members to build the houses without loans or do some short term loans. Some have their own banks / credit unions. Sadly, a lot of the plains tribes are not in that situation.

1) most tribes were sent away from cities which makes casinos problematic, but it didn't hurt on the natural resource front for some

2) I still think the tribal pact with North Dakota that you cannot directly pay members (imagine a business that couldn't pay its owner) is the purest form of evil