What is their position of the US Forrest Service...?
The short answer is this: They support things that are proven like wolves and bears. Things that are unproven are just unproven. They can't be expected to have an official position on the subject or any subject that remains unproven. For instance, I doubt they have an official position on ESP or ghosts. I say 'unproven' because that is the general consensus of science. It seems- due to the discovery of Lucy and others- science has moved from 'Bigfoot can't exist' to 'Bigfoot might exist but so far is unproven'.
If I went hunting and shot Bigfoot those government forces (US Forrest and so on) would go where the facts take them. 'They' would say Bigfoot exists as soon as they saw the body. They might be a local sheriff, some DNR guy, some US Forrest guy in a fire spotting tower, and 100 reporters who happen upon the story.
Someone in government making an April fool's joke about bigfoot doesn't change any position. I really don't think NORAD is trying to support or harm Christmas based on the Santa Tracker on Christmas eve.
There are some on the BFF and elsewhere who see the Government as some evil all powerful conspiracy about Bigfoot and about anything else they can image.
If you ask those type of people, they will attribute things to the government that take you down quite a bunny trail. This even assumes something and big as the government made up of many layers and employees are all going to move in unison under one group think direction. Not likely. Don't believe me? See how fast they are to down vote me for posting this post.
Even during the moon landing times, we had different factions who argued about the very mode we would take to even get to the moon. That is a simple unified goal fully funded and yet the various opinions and growing pains were evident.
Those who say the government knows all about Bigfoot being out there and, here is the key, they are keeping it hidden are ones who NEED to have this be the case. They require a certain view of Government who probably that has even more deeper intentions even beyond Bigfoot.
Sorry, I can't see it that way at least as it relates to Bigfoot.
The answer is Government, or the US Forrest Service probably have people who work in it that believe in Bigfoot and some that don't. Beyond that, they are concerned about Budgets, hunting season, litterbugs and Yogi bear stealing picnic baskets.