Purely random and controlled? No.
OTOH, that’s a completely weaselly way of claiming victory - unreasonable demands in the face of overwhelming evidence. Again, something anti-vaxxers and other conspiracy theorists engage in.
As for sufficient cites of several studies that should be sufficient, the CDC is willing to oblige.
That it’s an unpopular thing? Sure: http://onlinelibrary.wiley.com/doi/10.1111/j.1600-0528.2007.00373.x/abstract;jsessionid=DED9AC1860D9A2ED7F0C58FE1E3DBC9F.f04t04
That scientific consensus is that water fluoridation is a good option? The World Health Organization, for one.
Rely? I do no such thing. It might be a problem if that was the only basis for my argument. Which it is not.
I’ll note that nitpicking at the least little chink rather than the overwhelming evidence is rather a more telling problem.
ETA: I will note again, that for purposes of the OP and despite the digression, any link between fluoridation and Alzheimer’s will be tenuous, at best. Alzheimer’s is prevalent in roughly the same measure in the US and Western Europe despite differences in fluoridation regimes.