I agree with you-they need probable cause to arrest you.
If not-they might have an invalid arrest.
The answer given does not imply that an attorney-client relationship has been established and your best course of action is to have legal representation in this matter.
I read your previous questions and the attorney's answers and I believe what they were getting at, is that it would not be an "arrest" requiring probable cause, but rather an "investigatory detention" -- i.e., depending on circumstances, the police may be able to bring you to the police station to ascertain your identity.
Reasonable suspicion and probable cause are very fact-specific standards and are usually applied by a court in hindsight, after an arrest or some other action has been taken. It's impossible to give you a bright-line answer to this question because the answer will depend on all kinds of facts -- some which may be known to you; some which may only be known to the cops at this point.
For example, in a recent case decided in CA, the appellate court determined that "The amount of time Vasquez [the defendant] was detained—45 to 50 minutes before he was identified—was not unreasonable under the circumstances, which included impounding the car, and transporting Vasquez to the police station for identification. (See People v. Gomez (2004) 117 Cal.App.4th 531, 537-538 ["There is no fixed time limit for establishing the constitutionality of an investigatory detention. Rather, such a detention will be deemed unconstitutional `when extended beyond what is reasonably necessary under the circumstances that made its initiation permissible' "]; People v. Celis, supra, 33 Cal.4th at pp. 675-676 ["Of significance . . . are the facts known to the officers in determining whether their actions went beyond those necessary to effectuate the purpose of the stop, that is, to quickly dispel or confirm police suspicions of criminal activity"].)" The purpose and circumstances of the stop are going to determine the answer to your question.
I wish you luck.
You do not have to carry ID except in certain circumstances, which you already know.
You also do not have to identify yourself to police in every situation. But there are situations where refusing to identify yourself could justify the police in holding you to determine your identity.
They are technically required to have some justifiable reason for wanting to know your identity, but in reality, manufacturing probable cause is not that difficult.
I don't know why you are asking such a question, but in everyday practice, police officers don't typically stop random people without some sort of reason.