You're correct IFF the TOS constitute a valid contract. Contracts can be invalid for a number of reasons, including "one party wasn't made aware they were entering a contract".

>Yes, your click on "I agree to the TOS" is binding on you

There is no such button in this particular case.

>no, no one cares that you were closing your eyes or crossing your fingers or whatever.

This is a straw man. Nobody is claiming this.

>Your use of the service shows your agreement.

That very much depends.