I recognized that's actually kind of a rare thing, which doesn't make sense to me.

If money wasn't automatically taken from peoples paycheck for gambling in stocks with outlandish PE ratios today, and no real business in 2001, I doubt they'd sit down the weekend after pay day, shop for stocks, and place buy orders.  

It could appreciate but I consider that gambling.

If you get the chance come check out the place, you wont recognize it!

If you do equity only your basically gambling to some degree.Buying negative cash flow assets is better then not buying anything at all however.

Keep in mind that this only works if the properties are in the states that the Series LLC is recognized.

Just recognize most buyers of 4 units or less will want to use conventional financing at some point (even if purchased all cash) and using any other valuation than comps will not work with the conventional loan. 

That is not investing, that is gambling.  

Is there a law which specifies that I'd owe taxes on rents which the law does not recognize as mine?

Good for you for recognizing the power that RE has  to grow your wealth!