As far as I can tell, what's called "fake yuri" in English is generally what the word "yuri" itself is used to mean in Japanese.
So Yuruyuri is exactly what its title says it is.
Whereas if it were about actual lesbians it would be called something like "Crying Flowers."
Nah, "yuri" definitely refers to actual lesbian content (albeit usually of the idealised kind with a focus on "purity").
YuruYuri's title is accurate because the "yuru" part means "lighthearted", so it's telling you from the get-go that it's going to have yuri undertones but not really take any of it too seriously. The YuruYuri mangaka, Namori, actually also released a single-volume manga called "YuriYuri", which is exactly what the title would imply - a collection of short stories about actual lesbian relationships.
(Of course you fairly often see the word "yuri" attached to things that don't really contain proper lesbian content in the Japanese community for the same reason as you do in the English community - because people like to get their yuri goggles on =p)