The Eldar/Dark Eldar relationship has changed over the last few editions.
It used to be an extreme hatred towards one another, now however it seems that they merely have philosophical and lifestyle differences.
I feel that dropping it down a level would have made more sense, as the two factions have allied in the past. Both sides hate Chaos equally with a passion, and both sides recognize the potential threat of races like the tyranids and necrons. However classing them as Battle Brothers is I feel taking it a tad too far.
I don't agree with tyranids being left out. Between genestealer cults and Mind Control, there are enough justifications for them to use IG and Orks as unwilling pawns and fodder.
I agree that they're not utterly bitter rivals but making those two relationships as battle brothers seems off. As you say they should probably be one notch lower.
As for the tyranids, I think it's more of a factor that no other race would even begrudgingly ally themselves with the tyranids seeing as they're the Great Devourer. All tyranids do is consume (in one fashion or another) and I think they were going for something along the lines of having something that every other race could hate? Makes me wonder if that philosophy might change the nature of the other alliances. After all, the enemy of my enemy is my friend...right?