Value is only in the eye of the beholder.
There is no such thing as "inherent value" like taste, its all relative.
For example, $5 for a 1 litre bottle of water sounds expensive right? But if you're in the desert without any other water supply in range, its a bargain.
Twitter valued it because it convinced it's self it needed it. Its as simple as that, its the same logic that convinced HP to spunk out however much it was for autonomy, or News international for myspace.
Maybe they thought it was a good product, maybe they they knew the founders, maybe they talked a good game about facebook acquiring them. Either way it was valued that high not because it was a stunning product, but because twitter thought it needed that company and was prepared to spend 100million on it+.
+Yes that could be construed as cyclical login.