I agree with you and this is a reminder of how critical it is to use a different password for these accounts and for your email address. Because LinkedIn put what is essentially a fishing screen in front of you where they ask you for your email address and password. Now you can very easily have used your email address to log in to LinkedIn and therefore you can easily assume this is linked in asking you to relogin. What you don't realize is you're giving up your email address and email password if they have a good match what you think you're typing in to login to LinkedIn
Where do you go? I've hunted around a lot - it's really uncomfortable that they tell you "nothing is connected" and then recommend people you've dated...