Effy, I think the difference in our opinions about an LLC is in the semantics. Yes, an LLC can be used for business purposes but it can also be used for non-business purposes. I think you are taking the tact that the LLC MUST be used only in a business context and that is not the sole purpose of the LLC. The example of John Travolta's plane is the perfect example of using an LLC for non-business purposes.
As to the moral issue of not paying sales taxes when they are not owed, let's take a different approach. I think all of us would agree that Veteran's benefits should not be taxable. That being said, does anyone intentionally pay taxes on those benefits when no tax is owed? No one that I know does that and I certainly wouldn't expect anyone to pay taxes they don't owe.
My comment about buying a motorhome in another state through a Montana LLC and not paying NYS sales tax has to do with the unit not being "in service" in NY State. For example, if I have a summer home in Montana and I buy a car there and do not bring it into NY then there is no NY tax owed. If, however, I bring that car into NY and go to license it here, then I would owe the tax. I see this all the time with the snowbirds who buy cars in Florida and leave them there for the summer. They paid Florida sales tax because the vehicle is licensed and used in Florida but not NY tax even though they are legal residents of NY.