it's been quite a few years since I purchased anything but I believe the general theory was since "my" personal funds paid for the down payments and I personally hold the mortgages, the LLC doesn't stand on it's own and a good attorney will be able to "pierce" it's validity.
That doesn't sound right to me. That would invalidate the purpose of an LLC. Also, I had a C Corp and an LLC and was allowed to fund their operation for quite some time with personal funds without invalidating the corporation. LLC laws vary from state to state, and checking with an attorney on how to avoid the scenario shouldn't cost all that much. Even if you have to have the LLC hold on to some of it's "shares" and buy them periodically from the LLC, or something. I'm sure there's a way to do it. And yes I've seen many properties in an LLC with a mortgage. Here a quick claim deed is used to transfer title to the LLC and the mortgage is still intact. Again, check with the attorney on how to do that. It's worth a few dollars to get the right advice.