And if you want to get into sasquatch.. Though I realize it's slightly off topic, I think it serves a better example for why this line of thinking is so bad than time travel, which has little evidence to support it.
There exist very good reasons to suspect there did in fact exist a sasquatch in historical time, and those reasons boil down to simple parsimony. The stories of this creature/manlike-thing abound clear across North America, amongst completely separated peoples, and all the way into Central Asia. They are all pretty much the same thing.
Then you have historical accounts of these creature in our own nation's history. Settlers described them as wild men. You can go back to newspaper clippings from the 1800s and the stories recorded of these creatures are very similar to many of the reports we get today. The same kinds of behaviors: wood knocking, curiousity, the aggression, stealing things, etc.
That doesn't prove a damned thing definitively, but it does create a problem for Team Does Not Exist, since now they have to come up with some explanation for how completely isolated peoples spread across half the Earth's surface, and people spanning at least two centuries of recorded history describe the exact same creature. That's a little odd.
That you can put on a monkey suit and get shot in the national forest I think is amusing, but it does not somehow disprove a damned thing. There exist more reasons to believe this creature at least existed in the past than not.
Nor is this a scientific problem. Discovering a new species is not a science experiment. You have to go out and record the creature, collect physical evidence, run the DNA, and figure out what it is is, exactly. A scientific problem is something like do black holes produce thermal radiation, yes or no? If you take the negative, your statement is falsifiable by simply collective evidence of thermal radiation from a black hole. That is how falsifiability works.