No, they are not free to place someone under arrest. A law must have been broken (and not the one that has already been resolved with a ticket. You cannot ticket AND arrest for the same offense, one or the other) to warrant a NEW charge.
Signing a ticket is not an offense. Signature NOT required. This officer is a jerk and will be removed from the force. A cowboy with a badge.
What jurisdiction are you talking about? The standard protocol in the states with which I'm familiar is that the issuance of a citation is an arrest. At that point, you're given the option to sign a promise to appear in court, or to go into custody. The signature is your promise to appear, nothing more, nothing less. This guy chose option two.