You'll need to hire an attorney. You're correct that your cited statute does not require you to incriminate the other driver. If the court is requiring this, it may be acting beyond its authority. This means you'll need someone who is trained in law and advocacy to convince the court that it is wrong.
There was a discussion a while back on one of the criminal defense email list serves that courts are routinely requiring this, even though the statute does not. Thus, you may have a valid argument.
If you want to take care of this without hiring a lawyer, you can try arguing to the court yourself. However, if you get denied, the only way to get relief is to appeal that decision, which will cost money and add an additional level of complexity.
You can, of course, simply incriminate the other driver and give in to the court.
Either you or a lawyer will likely have to go to court to fight the ticket. We have cameras down here in Oregon though I haven't dealt with them in WA. In Portland, the city outsources the cameras to a private company. They send out all the tickets to the registered owner of the vehicle in the photo. If someone sends one of those affidavits back, the court will dismiss the ticket, but if the company takes another look at it, and it appears to match the profile of the driver, then they'll re-issue it and the person will have to come to court to show it wasn't them before they'll dismiss it. I think they cannot require you to incriminate someone else. But your way to not incriminate another person AND not pay the ticket may be to go to court and show them it's not you in the picture.
The law does not require a statement of who the other driver, but many courts ask for this information anyways. Many times, going to court is a better way to go because I have not seen the judge ask for the name of the driver (if it is known). That being said, these tickets are considered parking tickets, don't go on driving records, and don't get reported to insurance companies. If you wish to avoid paying the default, you must ask the court for a relief from judgment to make this happen.