In the US, the burden of proof in a civil case is distinct from that in a criminal case (it is true that in European systems, the plaintiff must prove their claims beyond reasonable doubt, but we're talking about US law here). The particular statute, RCW 46.63.075, does somewhat favor the state as plaintiff, stating that the automatic camera evidence
constitutes in evidence a prima facie presumption that the registered
owner of the vehicle was the person in control of the vehicle at the
point where, and for the time during which, the violation occurred.
The law further states that
This presumption may be overcome only if the registered owner states,
under oath, in a written statement to the court or in testimony before
the court that the vehicle involved was, at the time, stolen or in the
care, custody, or control of some person other than the registered
which means filling out a form like this. The form itself is plainly not illegal in any sense, the question is whether RCW 46.63.075 is in some sense illegal. This being a civil matter, guilt / innocence are irrelevant, and the burden of proof is not strongly on the plaintiff (the government). It is entirely legal for there to be a evidentiary presumption, as long as the presumption is defeasible. There could be a legal problem if it was impossible to satisfy the requirements for disproof, for instance if the condition was "upon order from the US Supreme Court". A requirement to appear in Lester municipal court within 1 hour would be practically impossible to satisfy.
A particular form might be "illegal" in the sense of not correctly stating the requirements of RCW 46.63.075, though again that just means that you have to appear in court to state the statutorily required fact rather than mailing in a form. That form seems to go somewhat beyond the requirement of the law in requiring all registered owners to sign the form when the statute refers to "the registered owner", but state law allows vacillation between singular and plural in interpreting laws, if required to make sense.
Bear in mind that RCW 46.63.075 only addresses the question of identifying the infractor, since in other moving infractions the officer can personally testify as to identity. You are still entitled to proffer other defenses such as that the camera does not prove that the alleged vehicle was involved. The one question worth considering is whether the form offers a false trichotomy, since there are other "it wasn't me" scenarios imaginable. For example, suppose you can prove that you were out of the country at the time and you don't know how the vehicle cam to be in that situation. You could check the "stolen" and "under other's control" boxes. There is no requirement that you additionally provide proof of the statement, you just have to make the statement.
If you actually know that the car was not under the control of another (stolen or otherwise), signing the statement is criminal perjury. The state would have to prove that you knew that the statement was false, which they could do if they can prove through some other means that you were driving and if they can prove your state of mind (not sleep-driving, not having an alternative personality, not simply forgetful). You are correct that there is no requirement in Washington to know at all times who is driving your vehicle.
The legislature deliberately passed a specific law that limits what would be an otherwise valid common law right to refute an argument for liability (to require the plaintiff to offer evidence). In addition, the legislature actually made it illegal for the government to provide better evidence out of privacy concerns, since under
RCW 46.63.170, the photo evidence cannot include the face of the driver.