It's true that aluminum oxide forms on the surface of the aluminum, and it is resistant to corrosion. Actually, that's sort of how stainless works, too. Stainless is treated (passivized) with nitric acid or other means before being put into production, which oxidizes the chromium and protects the underlying metal. And you're right, it is because aluminum is so much softer that using utensils on it would scratch the coating off.
In theory, lactic acid at room temperature is only mildly corrosive to aluminum oxide. It is drastically more corrosive at higher temps. Aluminum oxide is also not digestible by humans and passes through. Given all that, you will still get some aluminum leeched into your cheese. I don't know how much. Personally, I wouldn't do it, but that's the science behind aluminum materials with lactic acid.