I'm not sure where you are getting your information, but according tot the Olympic National Forest (where Mt Ellinor is located) website: "Leashed pets are allowed on trails in Olympic National Forest. "
http://www.nps.gov/olym/planyourvisit/pets.htm
Explain to me how I'm lying.
You posted a link to the National Park website, not the National Forest information which is confusing (but lying? of course not).
In general the NPS is very very strict about pets. The NFS allows them but is less strict. I would assume the TH has info stating the leash is required?