Maybe Ms. Barnard meant "antidisestablishmentarianism", allegedly the longest legitimate non-scientific word in the English language :-)
Her letter is odd in another way. I only know what I read on the Internet, but my understanding of various news articles is that the SCOTUS majority was taking a strong exception to broad interpretation of state constitution Blaine Amendments. I think Ms. Barnard got SCOTUS wrong.
On one hand, I don't think state funding should go to supporting religion. On the other hand, if this "free shredded tires" program was open to any public OR private school that met certain qualifications, and this religious school qualified, it is religious discrimination to tell the school "no" solely because it was church-owned.
Now comes the fun part: Lawyers arguing that if state-supplied shredded tires are okay, then x, y, z, aa, bb, and cc are okay, also.