The only extra information you would be volunteering is that you signed in to a specific website. In most cases, this is not really a big deal.
I get that people have different levels of trust for these services than I do. I'm just more cynical than most, I guess.
Or as the case of twitter demonstrates, you're also trusting all future owners of the Oauth provider, whoever they may be. If an erratic billionaire with a penchant for breaking the rules whenever it suits him buys your Oauth provider, who's to say what he'll do with his new access? He could treat your accounts as his personal toys. Better hope you don't earn his personal ire when he's on another wine and ambien bender.
If it's not a big deal, then why do they offer this service "for free"?
It's all part of their commercial panopticon. You're missing the forest for the trees.