1) If Sasquatches exist, reporting data alone demands they have existed on Fort Lewis, WA, at some point since the creation of Ft. Lewis as an Army post in 1917 (just 27 years after the end of the American Indian Wars). Reporting data strongly indicates that Ft. Lewis features an enduring population of these creatures passing through on a regular basis, and a century ago might well have had a decent resident population. There are documented reports of soldiers seeing them, and even shooting at them, as well as civilians on and around the post seeing them. Pierce County pretty much has the highest report counts in the BRFO database for the entire continent. The U.S. Army has every tool and asset necessary to "catch" the strongest physical evidence of these creatures, even back in the early days of the post, especially after a half century of chasing Indians around the continent. They also have the ability to do so secretly, both from the knowledge of the public, other government agencies, and even from the knowledge of most of the soldiers and officers on post.
2) The Army has a cultural attitude of superiority over their environment and informational security.......to the point of paranoia. It has been this way since even before the beginning of the U.S. Army's existence when it was still the British Army. If field commanders have Sasquatches running around their facilities, reports will reach people with authority, and some of them WILL utilize their assets to find out what is going on, then they WILL report their findings to their superiors. If told to stop their activities and keep their mouths shut, there is more than a fair chance that they will do as instructed.
3) Especially since the mid-1960's (50 years after Ft. Lewis was founded, and more than 50 years ago from today), the environmental movement is plenty of reason why a post commander would keep the existence of sasquatches downplayed, if not actively covering their existence up, especially on Army lands. There are also numerous other potential reasons, especially if they have determined that these creatures are primitive humans (as the Indians claim), having gone through Indian Wars for some 500 years now.
If Sasquatches exist, some within the U.S. Army know about it. You can take that to the bank.