After Discussions with OSPI, The Mariner Principal, and emails from Alison Brynelson & Pat Hegarty

From my conversation with OSPI:
If an exchange student is living within the school boundaries then the school will receive the same funding for them as for other students. There does not appear to be any funding-related reason why you would not want to have an exchange student at the school or would not be able to allow them.
My conversation with the school principal:
He was not aware of this situation with G., but he was sympathetic. He is limited in what he can do, since his bosses are already involved. But he also said that the school is officially "at capacity" but the current enrollment is LESS than last year. So for some reason capacity is SMALLER than in the past, despite the school just having had additions completed. So last year there were more students AND construction.
The response from Superintendent Brynelson:
She pretty much just said that she didn't know about it and it's not her responsibility. She cc'ed the person who was responsible, Pat Hegarty, Executive Director of Secondary Education.
The response from Pat Hegarty:
Dear Ms. Johnson:
Dr. Brynelson passed your email along to me as I oversee the work of our secondary schools, and this consideration typically comes through my office.
I am terribly sorry, but it does appear that the staff acted beyond their purview in accepting G.'s enrollment. The question of accepting students from exchange programs is always dependent on our annual determination regarding building capacity levels (part of policy 3142 that you referenced), and we have determined that our high schools are at capacity for this year. On the basis of this, and our continuing practice, I must again deny your request.
We do certainly have many instances where families have a wide variety of guardianship responsibilities and family structures, but in a case such as this we cannot sign onto the J1 visa or claim the student as a foreign exchange student.
I say this with the sincere compassion; you sought guidance at the school and came to discover it was flawed. I honor that our staff acted supportively, though sadly, they acted without decision-making authority. Even so, I cannot abrogate my responsibility to following our policy and practice, and therefore must deny your request.
Sincerely,
Pat Hegarty